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- 1. Describing Motion Introduction to Kinematics Stephen Taylor & Paul Wagenaar Canadian Academy, KobeDraft Presentation – will be updated staylor@canacad.ac.jp
- 2. How do you know that something is moving?Whee! By Todd Klassy, via the Physics Classroom Galleryhttp://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
- 3. 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?”Whee! By Todd Klassy, via the Physics Classroom Galleryhttp://www.flickr.com/photos/physicsclassroom/galleries/72157625424161192/
- 4. How can we describe movement?Usain Bolt’s 100m world record (not his false start!)http://www.youtube.com/watch?v=3nbjhpcZ9_g
- 5. How can we describe movement?http://www.youtube.com/watch?v=3nbjhpcZ9_gStrobe diagrams can be used to measure distance / time:Analyse this strobe diagram. What does it show? What are the dots? 0m 100m
- 6. How can we describe movement? Sketch a distance/ time graph for Bolt.http://www.youtube.com/watch?v=3nbjhpcZ9_g Strobe diagrams can be used to measure distance / time: Analyse this strobe diagram. What does it show? What are the dots? 0m 100m
- 7. Describing Motion Distance - how far an object travels along a path.
- 8. Which object is 2m away from the juggler? Juggler
- 9. Which object is 2m away from the juggler? Juggler Distance is not always enough!
- 10. How can someone run for 45 seconds butgo nowhere? (and they are not on a treadmill)
- 11. How can someone run for 45 seconds butgo nowhere? (and they are not on a treadmill)http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m12s
- 12. How can someone run for 45 seconds butgo nowhere? (and they are not on a treadmill) Sketch a distance/ time graph for Johnson.http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m12shttp://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m12s
- 13. How can someone run for 45 seconds butgo nowhere? (and they are not on a treadmill) Sketch a distance/ time graph for Johnson.http://www.youtube.com/watch?v=zbqy1Rpjgmw#t=2m12s Sketch a displacement/ time graph for Johnson. Distinguish between distance and displacement.
- 14. Describing Motion Distance - how far an object travels along a path. Displacement - the position of an object in reference to an origin or to a previous position. Scalars, such as distance, are non-directional measures of movement. Vectors, such as displacement, are directional. Which might be more important to a pilot?
- 15. What are the coordinates of these objects? Coordinates can be used to describe an objects position or displacement. 2mE, 1mN origin
- 16. 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 ______________________
- 17. 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
- 18. 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.
- 19. Which objects are:• 2.1m away from the origin at 14oN of East?• 5m away from the origin at 30oN of East?
- 20. Which objects are:• 2.1m away from the origin at 14oN of East?• 5m away from the origin at 30oN of East?
- 21. Magnitude and Direction tell us the displacement in terms ofthe most direct path. N E origin
- 22. Magnitude and Direction can also be represented by directedline segments (vector diagrams). N E 1m The direction (angle relative to the orientation) and magnitude (length of the vector) are important.
- 23. Which objects lie closest to these vectors?(directed line segments – hint, start at origin, length is important) A N E N B E N C E
- 24. Which objects lie closest to these vectors?(directed line segments – hint, start at origin, length is important) A N E N B E N C E
- 25. Three ways of describing displacementComponents (coordinates or directional descriptors)- e.g. 3mE, 2mN of originMagnitude and Direction- described, e.g. 2.1m 14oN of origin AVectors (directed line segments)- direction and magnitude are important N E
- 26. 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
- 27. 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
- 28. Ke$ha’s Day Out on Rokko Island N 1km1. 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. Wake up feeling like P Diddy $
- 29. Ke$ha’s Day Out on Rokko Island N 1km1. 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. Club Wake up feeling like P Diddy $ Clothes Pedicure
- 30. Ke$ha’s Day Out on Rokko Island N 1km1. Calculate: a. Total distance b. Total displacement c. Average speed d. Average velocity e. Average speed on the walk home. Club Wake up feeling like P Diddy $ Clothes2. Describe the displacement of the pedicurist from her house using: a. directed line segment Pedicure b. direction and magnitude
- 31. Kinematics in Sport Criterion E: Processing Data 1. Pick a short clip of a sequence of movements in a sport. It must be: • In a defined area (e.g. football field or floor gymnastics mat) • Multi-directional (not just linear) 2. Map out the area using graph paper, including scale and descriptor of direction 3. Analyse the video clip and try to plot the position of the object (or person) at each change in direction. Label clearly. 4. Describe the displacement of each move. N Use each of these tools at least twice in 4 0 your descriptions of the movements. Components (coordinates or directional descriptors) 3 Magnitude and Direction 6 described, e.g. 2.1m 14oN of origin Vectors (directed line segments) scale 1 direction and magnitude 2 5
- 32. 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 towards the sensor away from the sensor
- 33. 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 Slow constant motion towards the sensor Fast constant motion away from the sensor resting resting
- 34. 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 motionSave your graph and share itwith the group.Label the parts of the graph andadd it to your word doc forsubmission to Turnitin.
- 35. 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-1 (metres per second)Velocity is the rate of change of position of anobject – with direction. How fast is it moving in that direction? Velocity is a vector quantity. e.g. m s-1 East (metres per second to the East)
- 36. Calculating Speed & Velocity Distance Speed Or Δd Displacement v= Δt Time Velocity The delta symbol (Δ) is used to represent “change in”
- 37. Calculating Speed Δd At what speed did the object move away from the sensor? v= Δt Δd v= Δt
- 38. Calculating Speed Δd At what speed did the object move away from the sensor? v= Δt Δd Δt v=
- 39. Calculating Speed Δd At what speed did the object move away from the sensor? v= Δt Δd 2.5m – 1m = 1.5m 1.5m Δt 3s – 1s = 2s v= 2s
- 40. Calculating Speed Δd At what speed did the object move away from the sensor? v= Δt Δd 2.5m – 1m = 1.5m v= 1.5m = 0.75ms-1 Δt 3s – 1s = 2s 2s
- 41. Calculating Speed Δd At what speed did the object move away from the sensor? v= Δt Δd 2.5m – 1m = 1.5m “per second” v= 1.5m = 0.75ms-1 Δt 3s – 1s = 2s 2s (2d.p.)
- 42. Calculating Speed Δd At what speed did the object move toward the sensor? v= Δt Δd v= Δt
- 43. Calculating Speed Δd At what speed did the object move toward the sensor? v= Δt Δd Δt Δd v= Δt
- 44. Calculating Speed Δd At what speed did the object move toward the sensor? v= Δt Remember: speed is a scalar, not a vector, so direction is not important Δd (don’t use negatives) 2.5m – 1.75m = 0.75m Δt 7.5s – 6s = 1.5s v= 0.75m 1.5s = 0.5ms-1
- 45. Instantaneous Speed Δd Is the speed of an object at any given moment in time. v= Δt X X X X X
- 46. Instantaneous Speed Δd Is the speed of an object at any given moment in time. v= Δt X v = 0.00ms-1 X v = 0.5ms-1 X X v = 0.75ms-1 v = 0.00ms-1 X v = 0.00ms-1
- 47. Average Speed Δd Is the mean speed of an object over the whole journey. “mean” v= Δt Every movement adds to the total distance traveled Δd + Δd Δt = 10 seconds v= 1.5m + 0.75m 10s = 0.225ms-1
- 48. Calculating Velocity Δd At what velocity did the object move away from the sensor? v= Δt Δd v= Δt
- 49. Calculating Velocity Δd At what velocity did the object move away from the sensor? v= Δt Δd Δt v=
- 50. Calculating Velocity Δd At what velocity did the object move away from the sensor? v= Δt Δd 2.5m – 1m = 1.5m 1.5m Δt 3s – 1s = 2s v= 2s
- 51. Calculating Velocity Δd At what velocity did the object move away from the sensor? v= Δt When the person moves away from the sensor, distance and Δd displacement are the same. 2.5m – 1m = 1.5m v= 1.5m = 0.75ms-1 Δt 3s – 1s = 2s 2s (away from sensor)
- 52. Calculating Velocity Δd At what velocity did the object move away from the sensor? v= Δt When the person moves toward the sensor, displacement is lost. Δd 1.75m – 2.5m= -0.75m Δt v= 0.75m = -0.5ms -1 1.5s (toward sensor)
- 53. 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. North is positive. East is positive. South is positive. N
- 54. 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. North is positive. East is positive. South is positive. N +ve zero +ve -ve -ve
- 55. 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. North is positive. East is positive. South is positive. N +ve +ve +ve zero +ve -ve -ve -ve -ve +ve
- 56. 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. North is positive. East is positive. South is positive. N +ve +ve -ve zero +ve zero +ve -ve -ve -ve -ve +ve -ve +ve +ve
- 57. Instantaneous Velocity Δd Is the velocity of an object at any given moment in time. v= Δt X X X X
- 58. Instantaneous Velocity Δd Is the velocity of an object at any given moment in time. v= Δt X v = 0.00ms-1 X X v = 0.75ms-1 X v = 0.00ms-1
- 59. Instantaneous Velocity Δd Is the velocity of an object at any given moment in time. v= Δt X v = 0.00ms-1 X v = -0.5ms-1 X v = 0.75ms-1 Velocity is a vector. It is direction-specific. This point moving closer to the X origin can be negative. v = 0.00ms-1
- 60. Average Velocity Δd Is the mean velocity of an object over the whole journey. “mean” v= Δt v=
- 61. Average Velocity Δd Is the mean velocity of an object over the whole journey. “mean” v= Δt v= 1.75m – 1.00m = 0.075ms -1 10s (away from sensor) Δd Δt = 10 seconds
- 62. Comparing Speed and Velocity Δd Mean speed is non-directional. ∆d = all distances Mean velocity is directional. ∆d = total displacement v= Δt v= 0.225ms -1 Mean speed v= 0.075ms-1 (away from sensor) Mean velocity
- 63. Calculating Speed & Velocity ΔdCalculate the following in your write-ups. v= ΔtChallenge A: a) Your speed of movement away from the sensor b) Your average velocity over the 10-second runChallenge B: a) Your instantaneous velocity at any single point of constant motion b) b) Your average velocity over the 10-second runBall Challenge (coming up): a) Maximum velocity of the ball when falling b) Average velocity of the ball
- 64. 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.
- 65. Explain this! Distance from sensor (m) Velocity (ms-1)
- 66. Explain this! Distance from sensor (m) Changing direction Slowing Speeding up Going upwards Falling Speeding up Resting Caught Velocity (ms-1) Let go Speeding up Slowing Resting Changing direction Speeding up (falling) Caught
- 67. Walk This Way Submitting your workLab 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 notes to make sure you achieve a good grade
- 68. Work-done WednesdayBy the end of the lesson: • Complete the Walk This Way lab and submit your work • Self-assess using the highlight tool • Check your graphs for: • Titles, axes labeled, units, clear and sensible annotations • Be sure that your explanations demonstrate your understanding of: • The difference between distance and displacement • Velocity • Speed and velocity calculationsIf you are done: • Use the resources here to check your understanding: • http://i-biology.net/myp/intro-physics/describing-motion/ • Find out more about acceleration • Use graph paper to set your own questions on displacement, speed and velocity • Review all of the language used so far. Can you use it confidently?
- 69. Calculating values on a curve 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. Distance from sensor (m) What about here? X Time (s)
- 70. Calculating values on a curve 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. Distance from sensor (m) What about here? X A triangle is not representative of the curve! Time (s)
- 71. Calculating values on a curve 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. Distance from sensor (m) 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. X Time (s)
- 72. Calculating values on a curve 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. Distance from sensor (m) 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. X Now the triangle fits the point. Time (s)
- 73. Calculating values on a curve 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. Distance from sensor (m) 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. X Now the triangle fits the point. Time (s) Δd v= = (0.6m – 0.25m) (0.4s) = 0.875ms-1 Δt
- 74. 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.
- 75. Speed and Velocity Δd v= A ball is thrown up in the air and caught. Determine: Δt a. The instantaneous velocity of the ball at points A and B b. The average velocity of the ball. 2 B A 1 0 0.5 1 Time (s)
- 76. Velocity and Vectors Δd v= Velocity is a vector – it has direction. Δt 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. Describe the motion in these velocity vector diagrams:origin Positive velocity, increasing velocity. + origin originorigin +
- 77. Velocity and Vectors Δd v= Velocity is a vector – it has direction. Δt 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 Positive velocity, decreasing velocity. Negative velocity, increasing velocity. consistent points in time. The direction of the arrow is important. Describe the motion in these velocity vector diagrams:origin Positive velocity, increasing velocity. + Negative velocity, increasing velocity. origin origin Object moves quickly away from origin, slows,origin Positive velocity, decreasing velocity. + turns and speeds up on return to origin.
- 78. The birds are angry that the pigs destroyed theirVelocity and Vectors 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.Draw velocity vectors for each position of the angry bird to show its relative instantaneousvelocity. 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) 1.6m 55cm 7.5 m
- 79. 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.
- 80. 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.
- 81. Velocity and Vectors Draw velocity vector diagrams for each of these karts. 10kmh-1 16kmh-1 8kmh-1 20kmh-1 Use the known vector as the scale.
- 82. Velocity and Vectors Draw velocity vector diagrams for each of these karts. 10kmh-1 16kmh-1 8kmh-1 20kmh-1 Use the known vector as the scale.
- 83. 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
- 84. Velocity and Vectors A rugby ball is displaced according to the vector below, for 0.6 seconds. Determine the velocity of the ball. Δd 10 v= Δt = 0.6 = 16.7ms-1 (30o up and forwards) 2m 30o
- 85. RIC Roll: Drive Safe 1 mile = 1.61km What are the speed limits (kmh-1) where you live or come from? Why are they set to those values? How is it enforced? What are the penalties?http://www.youtube.com/watch?v=L7fhzDUOsxI Two basic methods are used to police speeding on the roads: - instantaneous velocity - average velocity over a longer journey As a group explain how they work and discuss the pros and cons of each. http://www.youtube.com/watch?v=Qm8yyl9ROEM
- 86. RIC Roll: Drive Safe Applying Science to Local Issues Lots of children and senior citizens live in Rokko Island City (RIC). As a group they are at greatest risk from injuries due to speeding cars. They have been complaining of a group of street-racers on the island who they think are driving too fast. Unfortunately budgets are tight and the police can only take action if the community are able to give them good information on the speed at which these racers are going. The city council’s RIC Roll: Drive Safe project aims to promote community participation in safe-speed road behaviour. They need your input in designing the project. Rokko Island City (inside the green belt), via GoogleMaps Your task: 80-minute project • Develop a simple method for judging the speed of a car as it passes anywhere within the green • Group method belt on the island. • Present at the end of class • It must be cheap and effective. • 1 slide maximum • It must be easily understood by kids and adults. • Outline method • It cannot make use of any technology other than • Evaluate limitations that which is available to most people. • It must have a foundation in our unit.
- 87. RIC Roll: Drive Safe Applying Science to Local Issues Record and calculate the instantaneous speed of 5 cars passing the school. How much variation is there within your group? Car 1 2 3 4 5 Person A Δd Person B Person C Mean Range v= Δt Limitations Effects on Results Solutions Evaluate the reliability of this method for estimating speed of cars.
- 88. RIC Roll: Drive Safe Applying Science to Local Issues The local speed limit is 40kmh-1. Δd v= If we adopt the method of putting markers at set distances along each road, can you rearrange the Δt equation so that local people can determine whether or not a car is speeding – just by counting?
- 89. RIC Roll: Drive Safe Applying Science to Local Issues The local speed limit is 40kmh-1. Δd v= If we adopt the method of putting markers at set distances along each road, can you rearrange the Δt equation so that local people can determine whether or not a car is speeding – just by counting? t.v = d Sampled distance (you decide) This example: 50m d t=v = 50m = 50m = 50m = 4.5s 40kmh-1 40 x 1000 ( ) 11.1ms-1 3600
- 90. RIC Roll: Drive Safe Applying Science to Local Issues Now have a go using this free app: http://itunes.apple.com/us/app/simple-radar-gun/id442734303?mt=8 Use the manual settings to enter your set distance. Press to start, release to stop. It is not really a radar gun, though it is a useful tool. Can you explain exactly how it works? Can you evaluate some limitations of the app?
- 91. Criterion A: One WorldRIC Roll: Drive Safe Criterion B: Communication in Science Lots of children and senior citizens live in Rokko Island City (RIC). As a group they are at greatest risk from injuries due to speeding cars. The city council’s RIC Roll: Drive Safe project aims to promote community participation in safe-speed road behaviour. The most effective consultancy team’s project proposal will be adopted. Key to success in the project: • a system which will allow all citizens to determine Rokko Island City (inside the green belt), via GoogleMaps the speed of a car • very low-budget but high-impact campaignIn your proposal presentation: • Clearly define the problem in the context of community safety. • Explain your method to measure speeding using only simple techniques that could be communicated to (and carried out by) the community. • Explain how safe driving could be promoted to the community. • Consider and evaluate your proposals from the point of view of One World.
- 92. RIC Roll: Drive SafeCriterion A: One World Criterion B: Communication in ScienceWhat is the issue in a local context and Your group must present the projecthow can Science be applied to it? proposal to the Rokko Island council.Devise a science-based speed-safety You must communicate the scientificcampaign. Evaluate its implications basis of your programme clearly, usingwithin at least two contexts (moral, textual and graphical media.ethical, social, economical, political)
- 93. Calculating Speed Practice 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? d v t b. Where are riders B and C when A has finished? 0 10km 20km B A C 12:00Cyclist clipart from: http://www.freeclipartnow.com/d/36116-1/cycling-fast-icon.jpg
- 94. 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. d v t 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
- 95. 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 85kmh-1 on the freeway? … experiencing turbulence on an aeroplane? … cruising at high altitude on an aeroplane? … slowing your bike to stop for a cat?
- 96. Acceleration is the rate of change in velocity of an object origin 30 60 90 120 150 180 Which cars are experiencing acceleration? Find out here: http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm Sketch distance – time graphs for each car (on the same axes) Distance What do the shapes of the lines tell us about the cars’ motion? Time
- 97. 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. Δv a= Δt
- 98. Acceleration Change in velocity Δv a= Δt = acceleration Initial velocity – final velocity (ms-1) Time (s) Change in time ms -2 “Metres per second per second”
- 99. Acceleration a = 3ms-2 Time (s) Velocity (ms-1) Velocity (ms-1) 0 0 1 2 3 0 4 0 1 2 3 4formula Time (s)
- 100. Acceleration a = 3ms-2 12 Time (s) Velocity (ms-1) 9 Velocity (ms-1) 0 0 6 1 3 2 6 3 3 9 0 4 12 0 1 2 3 4formula Time (s)
- 101. Acceleration a = 3ms-2 12 Time (s) Velocity (ms-1) 9 Velocity (ms-1) 0 0 6 1 3 2 6 3 3 9 0 4 12 0 1 2 3 4 Time (s)formula v = 3t 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?
- 102. Acceleration a = 3ms-2 A car accelerates at a constant rate of 3ms-2. 12 Time (s) Velocity Calculate its instantaneous velocity at 7.5s: (ms-1) -1 9 a. in ms Velocity (ms-1) 0 0 6 b. in kmh-1 1 3 2 6 3 Calculate the time taken to reach its 3 9 maximum velocity of 216kmh-1. 0 4 12 0 1 2 3 4formula v = 3t Time (s)
- 103. Acceleration a = 3ms-2 12Time (s) Velocity Displace- (ms-1) ment (m) 30 9 0 Velocity (ms-1) Displacement (m) 1 6 18 2 3 9 3 3 4 0 0 1 2 3 4 Time (s)formula Determine the velocity and displacement of the object each second. Plot the results on the graph. Compare the shapes of the two graphs.
- 104. Acceleration a = 3ms-2 12Time (s) Velocity Displace- (ms-1) ment (m) 30 9 0 0 Velocity (ms-1) Displacement (m) 1 3 6 18 2 6 3 9 3 9 3 4 12 0 0 1 2 3 4 Time (s)formula v = 3t 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.
- 105. Acceleration a = 3ms-2 12Time (s) Velocity Displace- (ms-1) ment (m) 30 9 0 0 0 Velocity (ms-1) Displacement (m) 1 3 3 6 18 2 6 9 3 9 3 9 18 3 4 12 30 0 0 1 2 3 4 Time (s)formula v = 3t 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.
- 106. Acceleration a = -2ms-2 Time (s) Velocity (ms-1) Velocity (ms-1) 0 10 1 2 3 0 4 0 1 2 3 4 Time (s)formula
- 107. Acceleration a = -2ms-2 Time (s) Velocity (ms-1) Velocity (ms-1) 0 10 1 8 2 6 3 4 0 4 2 0 1 2 3 4 Time (s)formula
- 108. Accelerationa = 2kmh-1s-1 Time (s) Velocity (kmh-1) 0 10 1 2 3 0 4 0 1 2 3 4 Time (s)formula
- 109. Accelerationa = 2kmh-1s-1 18 Time (s) Velocity (kmh-1) Velocity (kmh-1) 0 10 1 10 2 3 4 0 0 1 2 3 4formula Time (s)
- 110. How is it possible for an object moving at constant speed toexperience acceleration, but not anobject moving at constant velocity?
- 111. Rokko Liner Project Form a hypothesis. Describe the motion in some suitable format as you currently know it. Make approximate predictions on 1. time between each station (MP IC) and (IC IK) 2. wait time at IC 3. top speed between MP and IC 4. top speed between IC and IK 5. acceleration leaving a station 6. acceleration arriving at a station For variables, treat Independent Variable as time Dependent Variable as displacement or velocity
- 112. Rokko Liner Project Write-ups. Read through the instructions once more – carefully! By the end of today’s lesson: • Data processing is complete and graphs ready • Analysis of data has begun Draft stages:
- 113. http://i-biology.net/MYP
- 114. B A C velocity D G time E F C B Ddistance A E time

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