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Describing Motion 2012

The document provides an introduction to describing motion through kinematics. It discusses key concepts such as scalars and vectors, distance and displacement, speed and velocity. It presents various methods for describing displacement including using components, magnitude and direction, and vector diagrams. The document also examines how to calculate speed and velocity from changes in distance or displacement over time. Graphs such as distance-time and velocity-time graphs are introduced as ways to represent motion. Students are encouraged to practice these concepts through activities such as an orienteering course and analyzing motion data.

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Introduction to Kinematics by Stephen Taylor & Paul Wagenaar; overview of the course and its aim to inspire students.

Introduction to how motion is defined, the significance of kinematics, and the concept of motion as change.

Topics covered include scalars vs. vectors, distance vs. displacement, and methods to analyze motion.

Practical activities to understand motion through scalars and vectors, calculating distance, and designing courses.

Calculating average speed; practice problems involving cyclists and car speed limits to apply concepts.

Methods for measuring speed to check compliance with speed limits; evaluating data collection methods.

Using graphs to compare distance and displacement, understanding speed vs. velocity, and their calculations.

Defining and calculating instantaneous speed and velocity with examples of scalar and vector distinctions.

Introduction to acceleration, its calculations and implications in motion analysis.

Understanding how constant speed can yield acceleration when direction changes; application in a real-world context.

Comparative analysis of the speeds of athletes using graphical methods; assessment of velocity.

Reflective questions about learning outcomes, performance, and assessments related to the unit.

Practical exercises in displacement and velocity calculations, contextualized with fun scenarios.

Wrap-up of key concepts learned throughout the Kinematics course with reference to a relatable context.

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Describing Motion Introduction to Kinematics 2012-13 Stephen Taylor & Paul Wagenaar Canadian Academy, Kobe Canadian Academy inspires students to inquire, reflect and choose to compassionately impact the world throughout their lives.
How do you know that something is moving? Whee! By Todd Klassy, via the Physics Classroom Gallery http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
How do you know that something is moving? Motion is change. Mechanics is the Science of Motion. Kinematics is the science of describing motion using graphs, words, diagrams and calculations. Our unit question: “How can we describe change?” Significant concept: Change can be communicated using descriptions, graphical representations and quantities. Whee! By Todd Klassy, via the Physics Classroom Gallery http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
How can we describe change? Whee! By Todd Klassy, via the Physics Classroom Gallery http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/ • Distinguish between scalars and vectors. • Distinguish between distance and displacement. • Describe displacement of an object using components (coordinates), magnitude and direction and directed line segment vector diagrams. • Describe motion of an object in a given direction based on positive and negative displacement. • Calculate distance and displacement from a map. • Plot distance and displacement graphs from raw data or a strobe diagram • Distinguish between instantaneous and average speed/velocity. • Calculate average speed and velocity from a displacement-time graph or set of recorded data. • Analyze a displacement-time graph to show various types of motion (constant, resting, direction etc). • Analyze a velocity-time graph to describe changes in motion. • Draw and analyze vector diagrams to show velocity (magnitude and direction) • Convert velocity in km/h to m/s and vice-versa. • Calculate distance (displacement), speed (velocity) or time from a word equation giving other key information. • Define acceleration. • Calculate acceleration from a set of data. • Deduce a formula to determine instantaneous velocity from a given acceleration. • Explain why objects moving at constant speed can experience acceleration, but not those moving at constant velocity.
Where are we going? http://www.slideshare.net/gurustip/qr-orienteering-rokko-island Complete the QR Code orienteering course to learn about describing motion using: • scalars and vectors • components • magnitude and direction • directed line segments
North South EastWest “North of West” “East of North” “ South of East” “ West of South” “West of North” “South of West” “ East of South” “ North of East” Where are we going?
North South EastWest “North of West” “East of North” “ South of East” “ West of South” “West of North” “South of West” “ East of South” “ North of East” origin A B C D E F G m.socrative.com/student/ Room: N304
Three ways of describing displacement N E Components (coordinates or directional descriptors) - e.g. 3mE, 2mN of origin Magnitude and Direction - described, e.g. 2.1m 35oN of West Vectors (directed line segments) - direction and magnitude are important North West 3m 2m
Scalars vs Vectors Non-directional quantities Distance How far an object travels along a path Speed Rate of change of the position of an object, e.g. 20m/s Quantities with direction Displacement Position of an object in reference to an origin or previous position Velocity Rate of change of the position of an object in a given direction, e.g. 20m/s East “per unit time” v= Δd Δt Average speed or velocity Change in distance or displacement Change in time More scalars: Time Energy Mass Volume More vectors: Acceleration Force Electric field
Where are we going? Formative assessed task for Criterion E: Processing Data. As a group, present your completed course map, calculations and summary of what you learned on a poster. Comment on the reliability of the data. Individually design a new, 4-point course using all methods of describing displacement. Location 4 may not be back at the origin. Calculate total distance and displacement for the course.
Where are we going? Individually design a new, 4-point course. Draw vector diagrams on the map. Two moves must be described using components. Two moves must be described using magnitude and direction. Calculate total distance along vector diagrams. Calculate total displacement from the origin. This includes direction. Show all working. 1 2 3 4
http://www.youtube.com/watch?v=gWnfqSxp-Dc Unstoppable A runaway train with no brakes and a load of really dangerous chemicals is heading right for your town. How long have you got? What questions do you need to ask? Train cartoon from: http://www.mytrucks.co.uk/how_to_draw_a_steam_train.htm http://en.wikipedia.org/wiki/CSX_8888_incident
http://www.youtube.com/watch?v=gWnfqSxp-Dc Unstoppable A runaway train with no brakes and a load of really dangerous chemicals is heading right for your town. How long have you got? Train cartoon from: http://www.mytrucks.co.uk/how_to_draw_a_steam_train.htm A B 113.4km v t d 210m in 10s http://en.wikipedia.org/wiki/CSX_8888_incident x
How do I convert between m/s and km/h? km h =1 m s = m s
How do I convert between m/s and km/h? km h =1 m s = m s 1000 60 x 60 1000 3600. To convert from m/s to km/h, multiply by 3.6. To convert from km/s to m/s, divide by 3.6. 1 m/s = 3.6km/h km/hm/s x 3.6 ÷ 3.6
Calculating Speed Practice Cyclist clipart from: http://www.freeclipartnow.com/d/36116-1/cycling-fast-icon.jpg 1. Three cyclists are in a 20km road race. A has an average speed of 30kmh-1, B is 25kmh-1 and C 22kmh-1. The race begins at 12:00. a. What time does rider A complete the course? b. Where are riders B and C when A has finished? 12:00 0 20km10km AB C v t d
Calculating Speed Practice 2. The speed limit is 40kmh-1. A car drives out of the car park and covers 10m in just 3s. Calculate: a. The speed of the car in kmh-1. b. The car comes to a stretch of road which is 25m long. What is the minimum amount of time the car should to take to be under the speed limit? Car clipart from: http://www.freeclipartnow.com/transportation/cars/green-sports-car.jpg.html v t d
This is how far we’ve got.
Splish Splash MrT and Mr Condon go swimming in the 25m RICL pool. Mr C is way faster than MrT. Free swimmer clipart from: http://www.clker.com/clipart-swimming1.html How long does it take MrC to lap MrT? How would you work it out? 25m in 18s25m in 20s MrCMrT
Are drivers speeding outside school? http://www.youtube.com/watch?v=Qm8yyl9ROEM 1 mile = 1.61km The speed limit is 40km/h. Convert this to m/s. What are some of the One World issues related to speeding drivers? In what ways could science be used to catch or prevent speeding drivers?
Are drivers speeding outside school? Aim: Test a quick method using cones and timers to determine whether a car is speeding outside the school or not. The speed limit is 40km/h. • Choose one of the methods on the following slides. • Record as many cars as you can in 15 minutes. • Show working of your calculations. • Consider uncertainties and errors in your results. v= Δd Δt 20m Car Distance (m) ±0.1m Time (s) ± ____ s Speed m/s ± ___ Speed km/h ± ___ 1 20 2 20 3 20 4 20 5 20
Measure the time taken for cars to cover 20m. Record all cars passing school over a 15 minute period. Calculate each recording as m/s. Determine how many cars are breaking the speed limit of 40km/h. Show your working in the conversion from m/s to km/h. Calculate the minimum time a car must take to pass between the cones whilst remaining within the speed limit. Evaluate the method, noting limitations and possible improvements. Are drivers speeding outside school? v= Δd Δt 20m
Are drivers speeding outside school? v= Δd Δt Free app: http://itunes.apple.com/us/app/simple-radar- gun/id442734303?mt=8 20m Measure the speed of all the cars that pass by the school in a 15-minute period. Determine how many cars are breaking the speed limit of 40km/h. Outline the conversion the app uses to get from metres and seconds to km/h. Calculate each recording as m/s. Calculate the minimum time a car must take to pass between the cones whilst remaining within the speed limit. Evaluate the method, noting limitations and possible improvements.
The local speed limit is 40kmh-1. If we adopt the method of putting markers at set distances along each road, can you rearrange the equation so that local people can determine whether or not a car is speeding – just by counting? t.v = d t = d v v= Δd Δt Sampled distance (you decide) This example: 50m 50m 40kmh-1 50m 40 x 1000 3600( ) 50m 11.1ms-1 4.5s= = == Are drivers speeding outside school?
Are drivers speeding outside school? Evaluate the method: • Are data reliable? (enough repeats, acceptable uncertainty/error) • Are data valid? (did we measure what we set out to measure?) • What are the limitations of the method, how might they have impacted the results and how could they be improved?
Representing motion graphically Sketch two curves for Michael Johnson: • Distance/time • Displacement/time http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m18s Distinguish between distance and displacement. 0 4515 30 400 200 100 300 time (seconds) d(metres)
Walk This Way Using LoggerPro to generate distance/time graphs. Challenge 1: • Open the experiment “01b Graph Matching.cmbl” • Give everyone a chance to move themselves to follow the line as closely as possible. Make sure the motion sensor is aimed at the body the whole time. • Save some good examples and share them with the group. What does the line show? resting Fast constant motion Slow constant motion away from the sensor towards the sensor
Walk This Way Using LoggerPro to generate distance/time graphs. Challenge 1: • Open the experiment “01b Graph Matching.cmbl” • Give everyone a chance to move themselves to follow the line as closely as possible. Make sure the motion sensor is aimed at the body the whole time. • Save some good examples and share them with the group. What does the line show? resting resting resting Fast constant motion Slow constant motion away from the sensor towards the sensor
Walk This Way Using LoggerPro to generate distance/time graphs. Challenge 2: • Open the experiment “01a Graph Matching.cmbl” • Produce your own – differently-shaped - 10-second motion that includes all of the following characteristics: • Slow constant motion, fast constant motion and resting (constant zero motion) • Motion towards and away from the sensor • Acceleration • Changes in motion Save your graph and share it with the group. Label the parts of the graph and add it to your word doc for submission to Turnitin.
Speed or Velocity? Speed is the rate of change of position of an object. Over time How fast is it moving? Speed is a scalar quantity. e.g. m/s (metres per second) Velocity is the rate of change of position of an object – with direction. How fast is it moving in that direction? Velocity is a vector quantity. e.g. m/s East (metres per second to the East)
Warm-up questions 1. Your average speed on a 64m journey is 80kmh-1. How long does it take? 2. A duck is on a pond. It starts 8m from the North edge and and swims for 10 seconds. It finishes 2m North of the edge. a. What was its velocity? b. Draw a vector diagram to show its displacement.
Calculating Speed v= Δd Δt At what speed did the object move away from the sensor? v= Δd Δt
Calculating Speed v= Δd Δt At what speed did the object move away from the sensor? Δd Δt v=
Calculating Speed v= Δd Δt At what speed did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s
Calculating Speed v= Δd Δt At what speed did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s = 0.75m/s
Calculating Speed v= Δd Δt At what speed did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s = 0.75m/s (2d.p.)
Calculating Speed v= Δd Δt At what speed did the object move toward the sensor? v= Δt Δd
Calculating Speed v= Δd Δt At what speed did the object move toward the sensor? Δd Δt v= Δt Δd
Calculating Speed v= Δd Δt At what speed did the object move toward the sensor? 2.5m – 1.75m = 0.75m Δd Δt 7.5s – 6s = 1.5s v= 0.75m 1.5s = 0.5m/s Remember: speed is a scalar, not a vector, so direction is not important (don’t use negatives)
Instantaneous Speed v= Δd Δt Is the speed of an object at any given moment in time. X X X X X no line
Instantaneous Speed v= Δd Δt Is the speed of an object at any given moment in time. v = 0.5m/s v = 0.75m/s v = 0.00m/s v = 0.00m/s v = 0.00m/s X X X X X
Average Speed v= Δd Δt Is the mean speed of an object over the whole journey. v= 1.5m + 0.75m 10s = 0.225m/s ΔdΔd + Δt = 10 seconds “mean” Every movement adds to the total distance traveled
Calculating Velocity v= Δd Δt At what velocity did the object move away from the sensor? v= Δd Δt
Calculating Velocity v= Δd Δt At what velocity did the object move away from the sensor? Δd Δt v=
Calculating Velocity v= Δd Δt At what velocity did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s
Calculating Velocity v= Δd Δt At what velocity did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s = 0.75m/s(away from sensor) When the person moves away from the sensor, distance and displacement are the same.
Calculating Velocity v= Δd Δt At what velocity did the object move away from the sensor? 1.75m – 2.5m= -0.75m Δd Δt v= 0.75m 1.5s = -0.5ms-1 (toward sensor) When the person moves toward the sensor, displacement is lost.
Positives and Negatives in Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive.
Positives and Negatives in Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive. +ve +ve -ve -ve zero
Positives and Negatives in Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive. +ve +ve -ve -ve zero -ve -ve +ve +ve +ve
Positives and Negatives in Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive. +ve +ve -ve -ve zero -ve -ve +ve +ve +ve zero -ve -ve +ve +ve
Instantaneous Velocity v= Δd Δt Is the velocity of an object at any given moment in time. X X X X
Instantaneous Velocity v= Δd Δt Is the velocity of an object at any given moment in time. v = 0.75m/s v = 0.00m/s v = 0.00m/s X X X X
Instantaneous Velocity v= Δd Δt Is the velocity of an object at any given moment in time. v = -0.5m/s v = 0.75m/s v = 0.00m/s v = 0.00m/s X X X X Velocity is a vector. It is direction-specific. This point moving closer to the origin can be negative.
Average Velocity v= Δd Δt Is the mean velocity of an object over the whole journey. v= “mean”
Average Velocity v= Δd Δt Is the mean velocity of an object over the whole journey. v= 1.75m – 1.00m 10s = 0.075m/s Δd Δt = 10 seconds “mean” (away from sensor)
Comparing Speed and Velocity v= Δd Δt v= 0.075m/s (away from sensor) v= 0.225m/sMean speed Mean velocity Mean speed is non-directional. ∆d = all distances Mean velocity is directional. ∆d = total displacement
Calculating Speed & Velocity v= Δd Δt Calculate the following in your write-ups. Challenge A: a) Your speed of movement away from the sensor b) Your average velocity over the 10-second run Challenge B: a) Your instantaneous velocity at any single point of constant motion b) b) Your average velocity over the 10-second run Ball Challenge (coming up): a) Maximum velocity of the ball when falling b) Average velocity of the ball
Walk This Way Using LoggerPro to generate distance/time graphs. Ball Challenge: • Open the experiment “02 Ball.cmbl” • Position the motion sensor on the floor or table, facing up. • Hold the volleyball about 3m above the sensor • Have someone ready to catch the ball before it hits the sensor. • Start the sensor, drop and catch the ball. Do this a few times. • Save and label the two graphs: distance/time and velocity/time. • Use these in your write-up to explain what is meant by velocity.
Explain this! Distance from sensor (m) Velocity (ms-1)
Explain this! Distance from sensor (m) Velocity (ms-1) Speeding up Slowing Changing direction Speeding up (falling) Caught Changing direction Resting Resting Let go Going upwards Falling Speeding up Slowing Speeding up Caught
Walk This Way Submitting your work Lab report • Assessed for Criterion E: Processing Data • Complete all the work in the class period to avoid homework. • Self-assess the rubric using a highlighter tool before submission. • Submit to Turnitin.com Pay attention to the task- specific clarifications to make sure you achieve a good grade
Calculating values on a curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X What about here?
Calculating values on a curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X What about here? A triangle is not representative of the curve!
Calculating values on a curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X If we draw a tangent to the curve at the point of interest we can use the gradient of the line to calculate the speed or velocity of the object – at that moment in time.
Calculating values on a curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X Now the triangle fits the point. If we draw a tangent to the curve at the point of interest we can use the gradient of the line to calculate the speed or velocity of the object – at that moment in time.
Calculating values on a curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X If we draw a tangent to the curve at the point of interest we can use the line to calculate the speed or velocity of the object – at that moment in time. Now the triangle fits the point. v= Δd Δt (0.6m – 0.25m) (0.4s) = = 0.875m/s
This is a displacement-time graph for the One-Direction tour bus. • Did they really go in one direction? How do you know? • Calculate their velocity at 2s • Calculate their average velocity (over the whole journey)
Speed and Velocity A ball is thrown up in the air and caught. Determine: a. The instantaneous velocity of the ball at points A and B b. The average velocity of the ball. v= Δd Δt Time (s) 10.50 1 2 A B
Velocity and Vectors Velocity is a vector – it has direction. We can use velocity vector diagrams to describe motion. The lengths of the arrows are magnitude – a longer arrow means greater velocity and are to scale. The dots represent the object at consistent points in time. The direction of the arrow is important. v= Δd Δt Describe the motion in these velocity vector diagrams: + origin origin origin + origin + Positive velocity, increasing velocity.
Velocity and Vectors v= Δd Δt Describe the motion in these velocity vector diagrams: + origin origin origin + origin + Object moves quickly away from origin, slows, turns and speeds up on return to origin. Positive velocity, increasing velocity. Negative velocity, increasing velocity. Positive velocity, decreasing velocity. Velocity is a vector – it has direction. We can use velocity vector diagrams to describe motion. The lengths of the arrows are magnitude – a longer arrow means greater velocity and are to scale. The dots represent the object at consistent points in time. The direction of the arrow is important. Positivevelocity,decreasingvelocity. Negativevelocity,increasingvelocity.
Velocity and Vectors Draw velocity vectors for each position of the angry bird to show its relative instantaneous velocity. Use the first vector as a guide. The flight takes 2.3s. Calculate: • vertical displacement of the bird. • average velocity (up) of the bird. • average velocity (right) of the bird. • average overall velocity (include direction and magnitude) 55cm 1.6m 7.5 m The birds are angry that the pigs destroyed their nests – but luckily they have spotted a new nesting site. However, short-winged and poorly adapted to flight, they need to use a slingshot to get there.
Velocity and Vectors Draw velocity vectors for each position of the angry bird to show its relative instantaneous velocity. Use the first vector as a guide.
Velocity and Vectors Draw velocity vectors for each position of the angry bird to show its relative instantaneous velocity. Use the first vector as a guide. Remember that velocity vectors represent velocity – not distance. So it doesn’t matter if there is an object in the way – the velocity is the same until the moment of impact.
Velocity and Vectors Draw velocity vector diagrams for each of these karts. 10km/h 16km/h 8km/h 20km/h Use the known vector as the scale.
Velocity and Vectors Draw velocity vector diagrams for each of these karts. Use the known vector as the scale. 10km/h 16km/h 8km/h 20km/h
Velocity and Vectors A rugby ball is displaced according to the vector below, for 0.6 seconds. Determine the velocity of the ball. 2m 30o
Velocity and Vectors A rugby ball is displaced according to the vector below, for 0.6 seconds. Determine the velocity of the ball. 2m 30o v= Δd Δt = 10 0.6 = 16.7m/s (30o up and forwards)
What do you feel when… … playing on a swing? (You know you’re not too cool for that) … taking off on an aeroplane? … driving at a constant 85km/h on the freeway? … experiencing turbulence on an aeroplane? … cruising at high altitude on an aeroplane? … slowing your bike to stop for a cat?
Acceleration is the rate of change in velocity of an object Which cars are experiencing acceleration? Find out here: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm origin 30 60 90 120 150 180 Sketch distance – time graphs for each car (on the same axes) What do the shapes of the lines tell us about the cars’ motion? Distance Time
Acceleration is the rate of change in velocity of an object Acceleration can be positive (‘speeding up’) or negative (‘slowing down’). An object at rest has zero velocity and therefore zero acceleration. An object at constant speed in one direction is not changing its velocity and therefore has zero acceleration. Velocity is a vector – the rate of change of displacement of an object. Displacement and velocity are direction-dependent. Therefore, a change in direction is also a change in acceleration. a=Δv Δt
Acceleration a=Δv Δtacceleration Change in velocity Change in time = Initial velocity – final velocity (m/s) Time (s) m/s/s “Metres per second per second”
Acceleration a = 3m/s/s Time (s) Velocity (m/s) 0 0 1 2 3 4 formula 0 0 1 2 3 4 Velocity(ms-1) Time (s)
Acceleration a = 3m/s/s Time (s) Velocity (m/s) 0 0 1 3 2 6 3 9 4 12 formula 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s)
Acceleration a = 3m/s/s Time (s) Velocity (m/s) 0 0 1 3 2 6 3 9 4 12 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Time (s) The velocity – time graph is linear as it is constant acceleration. This means it is increasing its velocity by the same amount each time. What would the distance – time graph look like? Velocity(m/s)
Acceleration a = 3m/s/s Time (s) Velocity (m/s) 0 0 1 3 2 6 3 9 4 12 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Velocity(ms-1) Time (s) A car accelerates at a constant rate of 3m/s/s. Calculate its instantaneous velocity at 7.5s: a. in m/s b. in km/h Calculate the time taken to reach its maximum velocity of 216km/h.
Acceleration a = 3m/s Time (s) Velocity (m/s) Displace- ment (m) 0 1 2 3 4 formula 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s) Determine the velocity and displacement of the object each second. Plot the results on the graph. Compare the shapes of the two graphs. 3 9 18 30 Displacement(m)
Acceleration a = 3m/s Time (s) Velocity (m/s) Displace- ment (m) 0 0 1 3 2 6 3 9 4 12 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s) The displacement – time graph is curved as it is constant acceleration – the rate of change of displacement increases. This means it is increasing its velocity by the same amount each time. 3 9 18 30 Displacement(m)
Acceleration a = 3m/s/s Time (s) Velocity (m/s) Displace- ment (m) 0 0 0 1 3 3 2 6 9 3 9 18 4 12 30 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s) The displacement – time graph is curved as it is constant acceleration – the rate of change of displacement increases. This means it is increasing its velocity by the same amount each time. 3 9 18 30 Displacement(m)
Acceleration 0 0 1 2 3 4 Velocity(ms-1) Time (s) a = -2ms-2 Time (s) Velocity (ms-1) 0 10 1 2 3 4 formula
Acceleration 0 0 1 2 3 4 Velocity(ms-1) Time (s) a = -2ms-2 Time (s) Velocity (ms-1) 0 10 1 8 2 6 3 4 4 2 formula
Acceleration 0 0 1 2 3 4 Time (s) a = 2kmh-1s-1 Time (s) Velocity (kmh-1) 0 10 1 2 3 4 formula
Acceleration 0 0 1 2 3 4 Time (s) a = 2kmh-1s-1 Time (s) Velocity (kmh-1) 0 10 1 2 3 4 formula Velocity(kmh-1) 10 18
How is it possible for an object moving at constant speed to experience acceleration, but not an object moving at constant velocity?
How is it possible for an object moving at constant speed to experience acceleration, but not an object moving at constant velocity? Image: Moon from northern hemisphere: http://en.wikipedia.org/wiki/Moon
Who’s faster? Bolt vs Gump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196 http://www.youtube.com/watch?v=3nbjhpcZ9_g Usain Bolt’s 100m world record: 100m0m Gump Bolt Strobe diagram: each dot is the position of the runner after one second.
Graphing Motion Bolt vs Gump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196 100m0m Gump Bolt Sketch a distance/ time graph for Gump and Bolt. Strobe diagram: each dot is the position of the runner after one second.
Graphing Motion Bolt vs Gump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196 100m0m Gump Bolt Plot a distance/ time graph for Gump and Bolt. What other analysis can be carried out with these data? Discuss and do it! Strobe diagram: each dot is the position of the runner after one second.
Gump vs. Bolt Bolt vs Gump, from http://www.ew.com/ew/gallery /0,,20220853_20499114,00.htm l#20499196 Blog post: Describing Motion Review Use the Gump vs Bolt data to write a blog post. It will act as a review of the content of the unit (check the assessment statements on your review sheet), as well as an informative article for others. You can write it as: • A local reporter for the Greenbow, Alabama paper • A sports reporter writing about Bolt and the Olympics • A straight-up scientific explainer for HS students Look at the criteria and the assessment statements. As a small group, make and share a list of task-specific clarifications. Check, draft, write, cite. It will be assessed for Criterion B: Communication in Science:
Infographic from: http://www.telegraph.co.uk/sport/olympics/olympic_infographics_and_data/9453618/London-2012- Olympics-battle-of-the-sprint-kings-Usain-Bolt-and-Yohan-Blake.html Bolt vs Blake: What do the data tell us?
Unit Test: Describing Motion Criterion C: Knowledge & Understanding in Science
Unit Test: Describing Motion Criterion C: Knowledge & Understanding in Science Reflection on the back of the test: 1. What have you learned during this ‘Motion’ unit that you didn’t know before? 1. What have you learned about how you learn? 1. Do you think your performance in the test is a good reflection of your learning? Why? 1. Do you think the test was fair and allowed you to demonstrate what you had learned? How would you improve it? 1. How will you build on this for next time? If you’re done: • Rokko Liner Plans!
Rokko Liner Project
Spare Slides
time velocity A B C D E F G distance time A B C D E
What are the coordinates of these objects? origin 2mE, 1mN Coordinates can be used to describe an objects position or displacement.
Pick a mystery object. Describe the displacement to three other objects. Can another group deduce the objects? Example: From (mystery object) It is: • 1mE, 1mS to the ______________________ • 4mS to the ______________________ • 2mS, 4mE to the ______________________
Pick a mystery object. Describe the displacement to three other objects. Can another group deduce the objects? Example: From (mystery object) It is: • 1mE, 1mS to the Big Squirrel • 4mS to the Enthusiastic Runner • 2mS, 4mE to the Tiny Cyclist
Pick a mystery object. Describe the displacement to three other objects. Can another group deduce the objects? Example: From (Giant Acorn) It is: • 1mE, 1mS to the Big Squirrel • 4mS to the Enthusiastic Runner • 2mS, 4mE to the Tiny Cyclist The components (coordinates) of displacement tell us where the object has moved to overall, but they do not necessarily tell us the path it has taken.
Which objects are: • 2.1m away from the origin at 14oN of East? • 5m away from the origin at 30oN of East?
Which objects are: • 2.1m away from the origin at 14oN of East? • 5m away from the origin at 30oN of East?
Magnitude and Direction tell us the displacement in terms of the most direct path. E N origin
Magnitude and Direction can also be represented by directed line segments (vector diagrams). E N 1m The direction (angle relative to the orientation) and magnitude (length of the vector) are important.
Which objects lie closest to these vectors? (directed line segments – hint, start at origin, length is important) N E N E N E A B C
Which objects lie closest to these vectors? (directed line segments – hint, start at origin, length is important) N E N E N E A B C
Describing displacement N Components (coordinates or directional descriptors) - e.g. 3mE, 2mN of origin Magnitude and Direction - described, e.g. 2.1m 14oN of origin Vectors (directed line segments) - direction and magnitude are important
Describing displacement N Components (coordinates or directional descriptors) - e.g. 3mE, 2mN of origin Magnitude and Direction - described, e.g. 2.1m 14oN of origin Vectors (directed line segments) - direction and magnitude are important
1km N $ Ke$ha’s Day Out on Rokko Island Wake up feeling like P Diddy 1. Wake up in the morning (11am) feeling like P Diddy. 2. Get a pedicure, 5kmE 2.5kmS of home. 3. Then hit the clothes store, 30oNorth of East 5km away. 4. Cruise along, top down, CD’s on. Along this vector (directed line segment) to club. 5. Club closes 1am. Walk home. 6. Arrive home 4am by most direct route.
1km N $ Ke$ha’s Day Out on Rokko Island Wake up feeling like P Diddy 1. Wake up in the morning (11am) feeling like P Diddy. 2. Get a pedicure, 5kmE 2.5kmS of home. 3. Then hit the clothes store, 30oNorth of East 5km away. 4. Cruise along, top down, CD’s on. Along this vector (directed line segment) to club. 5. Club closes 1am. Walk home. 6. Arrive home 4am by most direct route. Pedicure Clothes Club
1km N $ Ke$ha’s Day Out on Rokko Island Wake up feeling like P Diddy 1. Calculate: a. Total distance b. Total displacement c. Average speed d. Average velocity e. Average speed on the walk home. 2. Describe the displacement of the pedicurist from her house using: a. directed line segment b. direction and magnitude Pedicure Clothes Club
Sketch a velocity-time graph for this journey. 0.5s 0.2m Calculate velocity before it hits the fabric.
Thrown up at 12m/s Accelerates down at 10m/s/s Hits water at 4s. What is the velocity as it hits the water? What is the height of the bridge?
Images adapted from http://www.fanpop.com/spots/one-direction/images/28558025/title & http://goo.gl/zJnql THE ONE DIRECTION TOUR BUS

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Describing Motion 2012

  • 1.
    Describing Motion Introduction toKinematics 2012-13 Stephen Taylor & Paul Wagenaar Canadian Academy, Kobe Canadian Academy inspires students to inquire, reflect and choose to compassionately impact the world throughout their lives.
  • 2.
    How do youknow that something is moving? Whee! By Todd Klassy, via the Physics Classroom Gallery http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
  • 3.
    How do youknow that something is moving? Motion is change. Mechanics is the Science of Motion. Kinematics is the science of describing motion using graphs, words, diagrams and calculations. Our unit question: “How can we describe change?” Significant concept: Change can be communicated using descriptions, graphical representations and quantities. Whee! By Todd Klassy, via the Physics Classroom Gallery http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
  • 4.
    How can wedescribe change? Whee! By Todd Klassy, via the Physics Classroom Gallery http://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/ • Distinguish between scalars and vectors. • Distinguish between distance and displacement. • Describe displacement of an object using components (coordinates), magnitude and direction and directed line segment vector diagrams. • Describe motion of an object in a given direction based on positive and negative displacement. • Calculate distance and displacement from a map. • Plot distance and displacement graphs from raw data or a strobe diagram • Distinguish between instantaneous and average speed/velocity. • Calculate average speed and velocity from a displacement-time graph or set of recorded data. • Analyze a displacement-time graph to show various types of motion (constant, resting, direction etc). • Analyze a velocity-time graph to describe changes in motion. • Draw and analyze vector diagrams to show velocity (magnitude and direction) • Convert velocity in km/h to m/s and vice-versa. • Calculate distance (displacement), speed (velocity) or time from a word equation giving other key information. • Define acceleration. • Calculate acceleration from a set of data. • Deduce a formula to determine instantaneous velocity from a given acceleration. • Explain why objects moving at constant speed can experience acceleration, but not those moving at constant velocity.
  • 5.
    Where are wegoing? http://www.slideshare.net/gurustip/qr-orienteering-rokko-island Complete the QR Code orienteering course to learn about describing motion using: • scalars and vectors • components • magnitude and direction • directed line segments
  • 6.
    North South EastWest “North of West” “Eastof North” “ South of East” “ West of South” “West of North” “South of West” “ East of South” “ North of East” Where are we going?
  • 7.
    North South EastWest “North of West” “Eastof North” “ South of East” “ West of South” “West of North” “South of West” “ East of South” “ North of East” origin A B C D E F G m.socrative.com/student/ Room: N304
  • 9.
    Three ways ofdescribing displacement N E Components (coordinates or directional descriptors) - e.g. 3mE, 2mN of origin Magnitude and Direction - described, e.g. 2.1m 35oN of West Vectors (directed line segments) - direction and magnitude are important North West 3m 2m
  • 10.
    Scalars vs Vectors Non-directionalquantities Distance How far an object travels along a path Speed Rate of change of the position of an object, e.g. 20m/s Quantities with direction Displacement Position of an object in reference to an origin or previous position Velocity Rate of change of the position of an object in a given direction, e.g. 20m/s East “per unit time” v= Δd Δt Average speed or velocity Change in distance or displacement Change in time More scalars: Time Energy Mass Volume More vectors: Acceleration Force Electric field
  • 11.
    Where are wegoing? Formative assessed task for Criterion E: Processing Data. As a group, present your completed course map, calculations and summary of what you learned on a poster. Comment on the reliability of the data. Individually design a new, 4-point course using all methods of describing displacement. Location 4 may not be back at the origin. Calculate total distance and displacement for the course.
  • 12.
    Where are wegoing? Individually design a new, 4-point course. Draw vector diagrams on the map. Two moves must be described using components. Two moves must be described using magnitude and direction. Calculate total distance along vector diagrams. Calculate total displacement from the origin. This includes direction. Show all working. 1 2 3 4
  • 13.
    http://www.youtube.com/watch?v=gWnfqSxp-Dc Unstoppable A runawaytrain with no brakes and a load of really dangerous chemicals is heading right for your town. How long have you got? What questions do you need to ask? Train cartoon from: http://www.mytrucks.co.uk/how_to_draw_a_steam_train.htm http://en.wikipedia.org/wiki/CSX_8888_incident
  • 14.
    http://www.youtube.com/watch?v=gWnfqSxp-Dc Unstoppable A runawaytrain with no brakes and a load of really dangerous chemicals is heading right for your town. How long have you got? Train cartoon from: http://www.mytrucks.co.uk/how_to_draw_a_steam_train.htm A B 113.4km v t d 210m in 10s http://en.wikipedia.org/wiki/CSX_8888_incident x
  • 15.
    How do Iconvert between m/s and km/h? km h =1 m s = m s
  • 16.
    How do Iconvert between m/s and km/h? km h =1 m s = m s 1000 60 x 60 1000 3600. To convert from m/s to km/h, multiply by 3.6. To convert from km/s to m/s, divide by 3.6. 1 m/s = 3.6km/h km/hm/s x 3.6 ÷ 3.6
  • 17.
    Calculating Speed Practice Cyclistclipart from: http://www.freeclipartnow.com/d/36116-1/cycling-fast-icon.jpg 1. Three cyclists are in a 20km road race. A has an average speed of 30kmh-1, B is 25kmh-1 and C 22kmh-1. The race begins at 12:00. a. What time does rider A complete the course? b. Where are riders B and C when A has finished? 12:00 0 20km10km AB C v t d
  • 18.
    Calculating Speed Practice 2.The speed limit is 40kmh-1. A car drives out of the car park and covers 10m in just 3s. Calculate: a. The speed of the car in kmh-1. b. The car comes to a stretch of road which is 25m long. What is the minimum amount of time the car should to take to be under the speed limit? Car clipart from: http://www.freeclipartnow.com/transportation/cars/green-sports-car.jpg.html v t d
  • 19.
    This is howfar we’ve got.
  • 20.
    Splish Splash MrTand Mr Condon go swimming in the 25m RICL pool. Mr C is way faster than MrT. Free swimmer clipart from: http://www.clker.com/clipart-swimming1.html How long does it take MrC to lap MrT? How would you work it out? 25m in 18s25m in 20s MrCMrT
  • 22.
    Are drivers speedingoutside school? http://www.youtube.com/watch?v=Qm8yyl9ROEM 1 mile = 1.61km The speed limit is 40km/h. Convert this to m/s. What are some of the One World issues related to speeding drivers? In what ways could science be used to catch or prevent speeding drivers?
  • 23.
    Are drivers speedingoutside school? Aim: Test a quick method using cones and timers to determine whether a car is speeding outside the school or not. The speed limit is 40km/h. • Choose one of the methods on the following slides. • Record as many cars as you can in 15 minutes. • Show working of your calculations. • Consider uncertainties and errors in your results. v= Δd Δt 20m Car Distance (m) ±0.1m Time (s) ± ____ s Speed m/s ± ___ Speed km/h ± ___ 1 20 2 20 3 20 4 20 5 20
  • 24.
    Measure the timetaken for cars to cover 20m. Record all cars passing school over a 15 minute period. Calculate each recording as m/s. Determine how many cars are breaking the speed limit of 40km/h. Show your working in the conversion from m/s to km/h. Calculate the minimum time a car must take to pass between the cones whilst remaining within the speed limit. Evaluate the method, noting limitations and possible improvements. Are drivers speeding outside school? v= Δd Δt 20m
  • 25.
    Are drivers speedingoutside school? v= Δd Δt Free app: http://itunes.apple.com/us/app/simple-radar- gun/id442734303?mt=8 20m Measure the speed of all the cars that pass by the school in a 15-minute period. Determine how many cars are breaking the speed limit of 40km/h. Outline the conversion the app uses to get from metres and seconds to km/h. Calculate each recording as m/s. Calculate the minimum time a car must take to pass between the cones whilst remaining within the speed limit. Evaluate the method, noting limitations and possible improvements.
  • 26.
    The local speedlimit is 40kmh-1. If we adopt the method of putting markers at set distances along each road, can you rearrange the equation so that local people can determine whether or not a car is speeding – just by counting? t.v = d t = d v v= Δd Δt Sampled distance (you decide) This example: 50m 50m 40kmh-1 50m 40 x 1000 3600( ) 50m 11.1ms-1 4.5s= = == Are drivers speeding outside school?
  • 27.
    Are drivers speedingoutside school? Evaluate the method: • Are data reliable? (enough repeats, acceptable uncertainty/error) • Are data valid? (did we measure what we set out to measure?) • What are the limitations of the method, how might they have impacted the results and how could they be improved?
  • 29.
    Representing motion graphically Sketchtwo curves for Michael Johnson: • Distance/time • Displacement/time http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m18s Distinguish between distance and displacement. 0 4515 30 400 200 100 300 time (seconds) d(metres)
  • 30.
    Walk This WayUsing LoggerPro to generate distance/time graphs. Challenge 1: • Open the experiment “01b Graph Matching.cmbl” • Give everyone a chance to move themselves to follow the line as closely as possible. Make sure the motion sensor is aimed at the body the whole time. • Save some good examples and share them with the group. What does the line show? resting Fast constant motion Slow constant motion away from the sensor towards the sensor
  • 31.
    Walk This WayUsing LoggerPro to generate distance/time graphs. Challenge 1: • Open the experiment “01b Graph Matching.cmbl” • Give everyone a chance to move themselves to follow the line as closely as possible. Make sure the motion sensor is aimed at the body the whole time. • Save some good examples and share them with the group. What does the line show? resting resting resting Fast constant motion Slow constant motion away from the sensor towards the sensor
  • 32.
    Walk This WayUsing LoggerPro to generate distance/time graphs. Challenge 2: • Open the experiment “01a Graph Matching.cmbl” • Produce your own – differently-shaped - 10-second motion that includes all of the following characteristics: • Slow constant motion, fast constant motion and resting (constant zero motion) • Motion towards and away from the sensor • Acceleration • Changes in motion Save your graph and share it with the group. Label the parts of the graph and add it to your word doc for submission to Turnitin.
  • 33.
    Speed or Velocity? Speedis the rate of change of position of an object. Over time How fast is it moving? Speed is a scalar quantity. e.g. m/s (metres per second) Velocity is the rate of change of position of an object – with direction. How fast is it moving in that direction? Velocity is a vector quantity. e.g. m/s East (metres per second to the East)
  • 34.
    Warm-up questions 1. Youraverage speed on a 64m journey is 80kmh-1. How long does it take? 2. A duck is on a pond. It starts 8m from the North edge and and swims for 10 seconds. It finishes 2m North of the edge. a. What was its velocity? b. Draw a vector diagram to show its displacement.
  • 35.
    Calculating Speed v= Δd Δt Atwhat speed did the object move away from the sensor? v= Δd Δt
  • 36.
    Calculating Speed v= Δd Δt Atwhat speed did the object move away from the sensor? Δd Δt v=
  • 37.
    Calculating Speed v= Δd Δt Atwhat speed did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s
  • 38.
    Calculating Speed v= Δd Δt Atwhat speed did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s = 0.75m/s
  • 39.
    Calculating Speed v= Δd Δt Atwhat speed did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s = 0.75m/s (2d.p.)
  • 40.
    Calculating Speed v= Δd Δt Atwhat speed did the object move toward the sensor? v= Δt Δd
  • 41.
    Calculating Speed v= Δd Δt Atwhat speed did the object move toward the sensor? Δd Δt v= Δt Δd
  • 42.
    Calculating Speed v= Δd Δt Atwhat speed did the object move toward the sensor? 2.5m – 1.75m = 0.75m Δd Δt 7.5s – 6s = 1.5s v= 0.75m 1.5s = 0.5m/s Remember: speed is a scalar, not a vector, so direction is not important (don’t use negatives)
  • 43.
    Instantaneous Speed v= Δd Δt Isthe speed of an object at any given moment in time. X X X X X no line
  • 44.
    Instantaneous Speed v= Δd Δt Isthe speed of an object at any given moment in time. v = 0.5m/s v = 0.75m/s v = 0.00m/s v = 0.00m/s v = 0.00m/s X X X X X
  • 45.
    Average Speed v= Δd Δt Isthe mean speed of an object over the whole journey. v= 1.5m + 0.75m 10s = 0.225m/s ΔdΔd + Δt = 10 seconds “mean” Every movement adds to the total distance traveled
  • 46.
    Calculating Velocity v= Δd Δt Atwhat velocity did the object move away from the sensor? v= Δd Δt
  • 47.
    Calculating Velocity v= Δd Δt Atwhat velocity did the object move away from the sensor? Δd Δt v=
  • 48.
    Calculating Velocity v= Δd Δt Atwhat velocity did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s
  • 49.
    Calculating Velocity v= Δd Δt Atwhat velocity did the object move away from the sensor? 2.5m – 1m = 1.5m Δd Δt 3s – 1s = 2s v= 1.5m 2s = 0.75m/s(away from sensor) When the person moves away from the sensor, distance and displacement are the same.
  • 50.
    Calculating Velocity v= Δd Δt Atwhat velocity did the object move away from the sensor? 1.75m – 2.5m= -0.75m Δd Δt v= 0.75m 1.5s = -0.5ms-1 (toward sensor) When the person moves toward the sensor, displacement is lost.
  • 51.
    Positives and Negativesin Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive.
  • 52.
    Positives and Negativesin Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive. +ve +ve -ve -ve zero
  • 53.
    Positives and Negativesin Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive. +ve +ve -ve -ve zero -ve -ve +ve +ve +ve
  • 54.
    Positives and Negativesin Velocity Velocity is direction-dependent. It can have positive and negative values. We can assign any one direction as being the positive. In the ball-throw examples, the data-logger has assigned movement away from the sensor (gaining displacement) as being the positive. Therefore movement towards the sensor is negative velocity. Identify which motions show positive, negative and zero velocity. NNorth is positive. East is positive. South is positive. +ve +ve -ve -ve zero -ve -ve +ve +ve +ve zero -ve -ve +ve +ve
  • 55.
    Instantaneous Velocity v= Δd Δt Isthe velocity of an object at any given moment in time. X X X X
  • 56.
    Instantaneous Velocity v= Δd Δt Isthe velocity of an object at any given moment in time. v = 0.75m/s v = 0.00m/s v = 0.00m/s X X X X
  • 57.
    Instantaneous Velocity v= Δd Δt Isthe velocity of an object at any given moment in time. v = -0.5m/s v = 0.75m/s v = 0.00m/s v = 0.00m/s X X X X Velocity is a vector. It is direction-specific. This point moving closer to the origin can be negative.
  • 58.
    Average Velocity v= Δd Δt Isthe mean velocity of an object over the whole journey. v= “mean”
  • 59.
    Average Velocity v= Δd Δt Isthe mean velocity of an object over the whole journey. v= 1.75m – 1.00m 10s = 0.075m/s Δd Δt = 10 seconds “mean” (away from sensor)
  • 60.
    Comparing Speed andVelocity v= Δd Δt v= 0.075m/s (away from sensor) v= 0.225m/sMean speed Mean velocity Mean speed is non-directional. ∆d = all distances Mean velocity is directional. ∆d = total displacement
  • 61.
    Calculating Speed &Velocity v= Δd Δt Calculate the following in your write-ups. Challenge A: a) Your speed of movement away from the sensor b) Your average velocity over the 10-second run Challenge B: a) Your instantaneous velocity at any single point of constant motion b) b) Your average velocity over the 10-second run Ball Challenge (coming up): a) Maximum velocity of the ball when falling b) Average velocity of the ball
  • 62.
    Walk This WayUsing LoggerPro to generate distance/time graphs. Ball Challenge: • Open the experiment “02 Ball.cmbl” • Position the motion sensor on the floor or table, facing up. • Hold the volleyball about 3m above the sensor • Have someone ready to catch the ball before it hits the sensor. • Start the sensor, drop and catch the ball. Do this a few times. • Save and label the two graphs: distance/time and velocity/time. • Use these in your write-up to explain what is meant by velocity.
  • 63.
    Explain this! Distance fromsensor (m) Velocity (ms-1)
  • 64.
    Explain this! Distance fromsensor (m) Velocity (ms-1) Speeding up Slowing Changing direction Speeding up (falling) Caught Changing direction Resting Resting Let go Going upwards Falling Speeding up Slowing Speeding up Caught
  • 65.
    Walk This WaySubmitting your work Lab report • Assessed for Criterion E: Processing Data • Complete all the work in the class period to avoid homework. • Self-assess the rubric using a highlighter tool before submission. • Submit to Turnitin.com Pay attention to the task- specific clarifications to make sure you achieve a good grade
  • 66.
    Calculating values ona curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X What about here?
  • 67.
    Calculating values ona curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X What about here? A triangle is not representative of the curve!
  • 68.
    Calculating values ona curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X If we draw a tangent to the curve at the point of interest we can use the gradient of the line to calculate the speed or velocity of the object – at that moment in time.
  • 69.
    Calculating values ona curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X Now the triangle fits the point. If we draw a tangent to the curve at the point of interest we can use the gradient of the line to calculate the speed or velocity of the object – at that moment in time.
  • 70.
    Calculating values ona curve Distance from sensor (m) Time (s) If we are calculating values of constant motion, life is easy. There is a straight line and we can draw a simple distance-time triangle to calculate speed or velocity. X If we draw a tangent to the curve at the point of interest we can use the line to calculate the speed or velocity of the object – at that moment in time. Now the triangle fits the point. v= Δd Δt (0.6m – 0.25m) (0.4s) = = 0.875m/s
  • 72.
    This is adisplacement-time graph for the One-Direction tour bus. • Did they really go in one direction? How do you know? • Calculate their velocity at 2s • Calculate their average velocity (over the whole journey)
  • 73.
    Speed and Velocity Aball is thrown up in the air and caught. Determine: a. The instantaneous velocity of the ball at points A and B b. The average velocity of the ball. v= Δd Δt Time (s) 10.50 1 2 A B
  • 74.
    Velocity and Vectors Velocityis a vector – it has direction. We can use velocity vector diagrams to describe motion. The lengths of the arrows are magnitude – a longer arrow means greater velocity and are to scale. The dots represent the object at consistent points in time. The direction of the arrow is important. v= Δd Δt Describe the motion in these velocity vector diagrams: + origin origin origin + origin + Positive velocity, increasing velocity.
  • 75.
    Velocity and Vectorsv= Δd Δt Describe the motion in these velocity vector diagrams: + origin origin origin + origin + Object moves quickly away from origin, slows, turns and speeds up on return to origin. Positive velocity, increasing velocity. Negative velocity, increasing velocity. Positive velocity, decreasing velocity. Velocity is a vector – it has direction. We can use velocity vector diagrams to describe motion. The lengths of the arrows are magnitude – a longer arrow means greater velocity and are to scale. The dots represent the object at consistent points in time. The direction of the arrow is important. Positivevelocity,decreasingvelocity. Negativevelocity,increasingvelocity.
  • 76.
    Velocity and Vectors Drawvelocity vectors for each position of the angry bird to show its relative instantaneous velocity. Use the first vector as a guide. The flight takes 2.3s. Calculate: • vertical displacement of the bird. • average velocity (up) of the bird. • average velocity (right) of the bird. • average overall velocity (include direction and magnitude) 55cm 1.6m 7.5 m The birds are angry that the pigs destroyed their nests – but luckily they have spotted a new nesting site. However, short-winged and poorly adapted to flight, they need to use a slingshot to get there.
  • 77.
    Velocity and Vectors Drawvelocity vectors for each position of the angry bird to show its relative instantaneous velocity. Use the first vector as a guide.
  • 78.
    Velocity and Vectors Drawvelocity vectors for each position of the angry bird to show its relative instantaneous velocity. Use the first vector as a guide. Remember that velocity vectors represent velocity – not distance. So it doesn’t matter if there is an object in the way – the velocity is the same until the moment of impact.
  • 79.
    Velocity and Vectors Drawvelocity vector diagrams for each of these karts. 10km/h 16km/h 8km/h 20km/h Use the known vector as the scale.
  • 80.
    Velocity and Vectors Drawvelocity vector diagrams for each of these karts. Use the known vector as the scale. 10km/h 16km/h 8km/h 20km/h
  • 81.
    Velocity and Vectors Arugby ball is displaced according to the vector below, for 0.6 seconds. Determine the velocity of the ball. 2m 30o
  • 82.
    Velocity and Vectors Arugby ball is displaced according to the vector below, for 0.6 seconds. Determine the velocity of the ball. 2m 30o v= Δd Δt = 10 0.6 = 16.7m/s (30o up and forwards)
  • 84.
    What do youfeel when… … playing on a swing? (You know you’re not too cool for that) … taking off on an aeroplane? … driving at a constant 85km/h on the freeway? … experiencing turbulence on an aeroplane? … cruising at high altitude on an aeroplane? … slowing your bike to stop for a cat?
  • 85.
    Acceleration is therate of change in velocity of an object Which cars are experiencing acceleration? Find out here: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm origin 30 60 90 120 150 180 Sketch distance – time graphs for each car (on the same axes) What do the shapes of the lines tell us about the cars’ motion? Distance Time
  • 86.
    Acceleration is therate of change in velocity of an object Acceleration can be positive (‘speeding up’) or negative (‘slowing down’). An object at rest has zero velocity and therefore zero acceleration. An object at constant speed in one direction is not changing its velocity and therefore has zero acceleration. Velocity is a vector – the rate of change of displacement of an object. Displacement and velocity are direction-dependent. Therefore, a change in direction is also a change in acceleration. a=Δv Δt
  • 87.
    Acceleration a=Δv Δtacceleration Change in velocity Changein time = Initial velocity – final velocity (m/s) Time (s) m/s/s “Metres per second per second”
  • 88.
    Acceleration a = 3m/s/s Time(s) Velocity (m/s) 0 0 1 2 3 4 formula 0 0 1 2 3 4 Velocity(ms-1) Time (s)
  • 89.
    Acceleration a = 3m/s/s Time(s) Velocity (m/s) 0 0 1 3 2 6 3 9 4 12 formula 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s)
  • 90.
    Acceleration a = 3m/s/s Time(s) Velocity (m/s) 0 0 1 3 2 6 3 9 4 12 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Time (s) The velocity – time graph is linear as it is constant acceleration. This means it is increasing its velocity by the same amount each time. What would the distance – time graph look like? Velocity(m/s)
  • 91.
    Acceleration a = 3m/s/s Time(s) Velocity (m/s) 0 0 1 3 2 6 3 9 4 12 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Velocity(ms-1) Time (s) A car accelerates at a constant rate of 3m/s/s. Calculate its instantaneous velocity at 7.5s: a. in m/s b. in km/h Calculate the time taken to reach its maximum velocity of 216km/h.
  • 92.
    Acceleration a = 3m/s Time(s) Velocity (m/s) Displace- ment (m) 0 1 2 3 4 formula 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s) Determine the velocity and displacement of the object each second. Plot the results on the graph. Compare the shapes of the two graphs. 3 9 18 30 Displacement(m)
  • 93.
    Acceleration a = 3m/s Time(s) Velocity (m/s) Displace- ment (m) 0 0 1 3 2 6 3 9 4 12 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s) The displacement – time graph is curved as it is constant acceleration – the rate of change of displacement increases. This means it is increasing its velocity by the same amount each time. 3 9 18 30 Displacement(m)
  • 94.
    Acceleration a = 3m/s/s Time(s) Velocity (m/s) Displace- ment (m) 0 0 0 1 3 3 2 6 9 3 9 18 4 12 30 formula v = 3t 12 9 3 0 6 0 1 2 3 4 Velocity(m/s) Time (s) The displacement – time graph is curved as it is constant acceleration – the rate of change of displacement increases. This means it is increasing its velocity by the same amount each time. 3 9 18 30 Displacement(m)
  • 95.
    Acceleration 0 0 1 23 4 Velocity(ms-1) Time (s) a = -2ms-2 Time (s) Velocity (ms-1) 0 10 1 2 3 4 formula
  • 96.
    Acceleration 0 0 1 23 4 Velocity(ms-1) Time (s) a = -2ms-2 Time (s) Velocity (ms-1) 0 10 1 8 2 6 3 4 4 2 formula
  • 97.
    Acceleration 0 0 1 23 4 Time (s) a = 2kmh-1s-1 Time (s) Velocity (kmh-1) 0 10 1 2 3 4 formula
  • 98.
    Acceleration 0 0 1 23 4 Time (s) a = 2kmh-1s-1 Time (s) Velocity (kmh-1) 0 10 1 2 3 4 formula Velocity(kmh-1) 10 18
  • 99.
    How is itpossible for an object moving at constant speed to experience acceleration, but not an object moving at constant velocity?
  • 100.
    How is itpossible for an object moving at constant speed to experience acceleration, but not an object moving at constant velocity? Image: Moon from northern hemisphere: http://en.wikipedia.org/wiki/Moon
  • 101.
    Who’s faster? Bolt vsGump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196 http://www.youtube.com/watch?v=3nbjhpcZ9_g Usain Bolt’s 100m world record: 100m0m Gump Bolt Strobe diagram: each dot is the position of the runner after one second.
  • 102.
    Graphing Motion Bolt vsGump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196 100m0m Gump Bolt Sketch a distance/ time graph for Gump and Bolt. Strobe diagram: each dot is the position of the runner after one second.
  • 103.
    Graphing Motion Bolt vsGump, from http://www.ew.com/ew/gallery/0,,20220853_20499114,00.html#20499196 100m0m Gump Bolt Plot a distance/ time graph for Gump and Bolt. What other analysis can be carried out with these data? Discuss and do it! Strobe diagram: each dot is the position of the runner after one second.
  • 104.
    Gump vs. Bolt Boltvs Gump, from http://www.ew.com/ew/gallery /0,,20220853_20499114,00.htm l#20499196 Blog post: Describing Motion Review Use the Gump vs Bolt data to write a blog post. It will act as a review of the content of the unit (check the assessment statements on your review sheet), as well as an informative article for others. You can write it as: • A local reporter for the Greenbow, Alabama paper • A sports reporter writing about Bolt and the Olympics • A straight-up scientific explainer for HS students Look at the criteria and the assessment statements. As a small group, make and share a list of task-specific clarifications. Check, draft, write, cite. It will be assessed for Criterion B: Communication in Science:
  • 105.
  • 106.
    Unit Test: DescribingMotion Criterion C: Knowledge & Understanding in Science
  • 107.
    Unit Test: DescribingMotion Criterion C: Knowledge & Understanding in Science Reflection on the back of the test: 1. What have you learned during this ‘Motion’ unit that you didn’t know before? 1. What have you learned about how you learn? 1. Do you think your performance in the test is a good reflection of your learning? Why? 1. Do you think the test was fair and allowed you to demonstrate what you had learned? How would you improve it? 1. How will you build on this for next time? If you’re done: • Rokko Liner Plans!
  • 108.
  • 109.
  • 110.
  • 111.
    What are thecoordinates of these objects? origin 2mE, 1mN Coordinates can be used to describe an objects position or displacement.
  • 112.
    Pick a mysteryobject. Describe the displacement to three other objects. Can another group deduce the objects? Example: From (mystery object) It is: • 1mE, 1mS to the ______________________ • 4mS to the ______________________ • 2mS, 4mE to the ______________________
  • 113.
    Pick a mysteryobject. Describe the displacement to three other objects. Can another group deduce the objects? Example: From (mystery object) It is: • 1mE, 1mS to the Big Squirrel • 4mS to the Enthusiastic Runner • 2mS, 4mE to the Tiny Cyclist
  • 114.
    Pick a mysteryobject. Describe the displacement to three other objects. Can another group deduce the objects? Example: From (Giant Acorn) It is: • 1mE, 1mS to the Big Squirrel • 4mS to the Enthusiastic Runner • 2mS, 4mE to the Tiny Cyclist The components (coordinates) of displacement tell us where the object has moved to overall, but they do not necessarily tell us the path it has taken.
  • 115.
    Which objects are: •2.1m away from the origin at 14oN of East? • 5m away from the origin at 30oN of East?
  • 116.
    Which objects are: •2.1m away from the origin at 14oN of East? • 5m away from the origin at 30oN of East?
  • 117.
    Magnitude and Directiontell us the displacement in terms of the most direct path. E N origin
  • 118.
    Magnitude and Directioncan also be represented by directed line segments (vector diagrams). E N 1m The direction (angle relative to the orientation) and magnitude (length of the vector) are important.
  • 119.
    Which objects lieclosest to these vectors? (directed line segments – hint, start at origin, length is important) N E N E N E A B C
  • 120.
    Which objects lieclosest to these vectors? (directed line segments – hint, start at origin, length is important) N E N E N E A B C
  • 121.
    Describing displacement N Components (coordinatesor directional descriptors) - e.g. 3mE, 2mN of origin Magnitude and Direction - described, e.g. 2.1m 14oN of origin Vectors (directed line segments) - direction and magnitude are important
  • 122.
    Describing displacement N Components (coordinatesor directional descriptors) - e.g. 3mE, 2mN of origin Magnitude and Direction - described, e.g. 2.1m 14oN of origin Vectors (directed line segments) - direction and magnitude are important
  • 123.
    1km N $ Ke$ha’s Day Outon Rokko Island Wake up feeling like P Diddy 1. Wake up in the morning (11am) feeling like P Diddy. 2. Get a pedicure, 5kmE 2.5kmS of home. 3. Then hit the clothes store, 30oNorth of East 5km away. 4. Cruise along, top down, CD’s on. Along this vector (directed line segment) to club. 5. Club closes 1am. Walk home. 6. Arrive home 4am by most direct route.
  • 124.
    1km N $ Ke$ha’s Day Outon Rokko Island Wake up feeling like P Diddy 1. Wake up in the morning (11am) feeling like P Diddy. 2. Get a pedicure, 5kmE 2.5kmS of home. 3. Then hit the clothes store, 30oNorth of East 5km away. 4. Cruise along, top down, CD’s on. Along this vector (directed line segment) to club. 5. Club closes 1am. Walk home. 6. Arrive home 4am by most direct route. Pedicure Clothes Club
  • 125.
    1km N $ Ke$ha’s Day Outon Rokko Island Wake up feeling like P Diddy 1. Calculate: a. Total distance b. Total displacement c. Average speed d. Average velocity e. Average speed on the walk home. 2. Describe the displacement of the pedicurist from her house using: a. directed line segment b. direction and magnitude Pedicure Clothes Club
  • 126.
    Sketch a velocity-timegraph for this journey. 0.5s 0.2m Calculate velocity before it hits the fabric.
  • 127.
    Thrown up at12m/s Accelerates down at 10m/s/s Hits water at 4s. What is the velocity as it hits the water? What is the height of the bridge?
  • 128.
    Images adapted fromhttp://www.fanpop.com/spots/one-direction/images/28558025/title & http://goo.gl/zJnql THE ONE DIRECTION TOUR BUS