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# Unit 2

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### Unit 2

1. 1. PHYSICS Matters for GCE ‘O’ Level Unit 2: Kinematics
2. 2. 2.1 Distance, Time and Speed In this section, you’ll be able to: • state what speed is • calculate average speed • plot and interpret a distance-time graph Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
3. 3. 2.1 Distance, Time and Speed What is Speed? Speed is the distance moved per unit time i.e. Speed = In symbols, v = where distance moved time taken d t d = distance moved (m) t = time taken (s) v = speed (m s-1) Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
4. 4. 2.1 Distance, Time and Speed The ‘Triangle’ Method To find the value of a quantity, cover up the symbol to give the related formula: • d=vt • v= d t • t= d v Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
5. 5. 2.1 Distance, Time and Speed What is Average Speed? Can you calculate the speed of each athlete in the table below? Athlete Event Time Speed/m s–1 Atlanta, 1996 Bailey, Canada 100 m 9.84 s 10.2 Atlanta, 1996 Johnson, USA 200 m 19.32 s 10.4 Atlanta, 1996 Johnson, USA 400 m 43.49 s 9.2 Atlanta, 1996 Rodal, Norway 800 m 1:42.59 min 7.8 Location, year Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
6. 6. 2.1 Distance, Time and Speed What is Average Speed? • The speed that you have calculated for each athlete is actually the average speed. • Each athlete did not run at the same speed throughout the race. • In short, average speed assumes that the object travels at the same speed throughout the entire distance. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
7. 7. 2.1 Distance, Time and Speed What is 1 m s-1 in km h-1? 1 m s-1 means that the object moves 1 m in 1 s. In 1 h, there are 60 × 60 = 3600 s. Hence, the distance traveled in 3600 s is 3600 m = 3.6 km. Therefore, 1 m s-1 = 3.6 km h-1. Or you can use conversion of units as follows: 1 m  1 km  60 s  60 min = 3.6 km = 3.6 km h-1 1 s 1000 m 1 min 1h 1h Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
8. 8. 2.1 Distance, Time and Speed Distance-time graphs For an object moving with constant or uniform speed, the distance-time graph is a straight line. What is the speed of this object? Distance/m 100 80 60 40 20 0 2 4 6 8 10 12 The total distance moved after 10 s is 80 m. Therefore, the speed is: 80 v= = 8 m s-1 10 Time/s Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
9. 9. 2.1 Distance, Time and Speed Distance-time graphs for increasing speed After 10 s, distance moved is 20 m. Average speed after 10 s is : 20 v= = 2 m s–1 10 100 80 60 40 20 0 2 4 6 8 10 12 14 16 Time/s Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 18 20 After 20 s, distance moved is 80 m. The average speed after 20 s is: 80 v= = 4 m s–1 20 4 February 2014
10. 10. 2.1 Distance, Time and Speed Distance-time graphs for decreasing speed During the first 18 s, the speed of the object decreases. 100 80 60 40 20 0 2 4 6 8 10 12 14 Time/s 16 18 Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. After 18 s, distance moved remains 100 m. There is no change in the distance from 10 s to 15 s. Therefore, the 20 speed is zero. The object is stationary or at rest. 4 February 2014
11. 11. 2.1 Distance, Time and Speed Instantaneous Speed The instantaneous speed of an object is the speed at a particular instant. It can be found from the gradient of the tangent at a point on the distance-time graph. At t = 5 s, the instantaneous speed is s 90 v= = 14 = 6.4 m s-1 t 100 80 60 40 s 20 0 t 2 4 6 8 10 12 14 Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 16 18 20 Time/s 4 February 2014
12. 12. 2.1 Distance, Time and Speed Key Ideas • Speed is the change in distance per unit time, v = s t Its SI unit is m s-1. • Average speed is the total distance travelled, divided by the total time taken. • A distance-time graph shows how distance changes with time. (a) If speed is uniform, the graph is a straight line. (b) If speed is non-uniform, the graph is a curve. • The gradient of the tangent at a point on the s-t graph gives the instantaneous speed. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
13. 13. 2.1 Distance, Time and Speed Test Yourself 2.1 At the start of a journey, the odometer (a meter which clocks the total distance of a car has travelled) has an initial reading of 50780 km. At the end of the journey, the odometer reading was 50924 km. The journey took two hours. What was the average speed of the journey in (a) km h-1 ? (b) m s-1 ? Speedometer Odometer Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
14. 14. 2.2 Speed, Velocity and Acceleration In this section, you’ll be able to: • state what velocity and uniform acceleration are change in velocity • calculate acceleration using Time taken • interpret given examples of non-uniform acceleration Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
15. 15. 2.2 Speed, Velocity and Acceleration Speed and Velocity Velocity is the change in distance in a specified direction (i.e. displacement) per unit time. It can be positive or negative. For example, when you perform a 200 m sprint, your distance is 200 m, whereas your displacement is generally Distance less, as shown in the figure below. What would your speed and velocity be when you run the 200 metres in Displacement 50 m 25 seconds? Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. travelled 200 m 4 February 2014
16. 16. 2.2 Speed, Velocity and Acceleration Acceleration Acceleration is the change in velocity with time. In symbols: a =  v (in m s-2) t 3 seconds after take off, a shuttle has a speed of 45 m s-1. What is its acceleration? Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
17. 17. 2.2 Speed, Velocity and Acceleration Key Ideas • Velocity is the change in displacement per unit time. It is speed in a specified direction. Its SI unit is m s-1, which is the same for speed. • Acceleration is the change in velocity per unit time. Its SI unit is m s-2. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
18. 18. 2.2 Speed, Velocity and Acceleration Test Yourself: Inside Scoop Ever heard of the Vertical Marathon? Since 1987, this race takes place annually at the tallest hotel in Southeast Asia: the 226 metres high Stamford hotel in Singapore. Balvinder Singh set the record in 1989 by climbing the 1336 steps in 6 minutes and 55 seconds. Calculate his velocity in steps and in kilometres per hour. Is his velocity positive or negative? Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
19. 19. 2.3 Speed-Time Graphs In this section, you’ll be able to: • plot and interpret speed-time graphs • determine the distance travelled by calculating the area under the speed-time graph Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
20. 20. 2.3 Speed-Time Graphs Uniform acceleration In a speed-time graph, a straight line denotes uniform acceleration. How can you achieve uniform acceleration when playing a racing game in an arcade? Answer: by stepping on the pedal all the way! On the next slide we can see the corresponding speed-time graph. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
21. 21. 2.3 Speed-Time Graphs Uniform acceleration Speed/m s-1 35 30 25 20 15 10 5 0 0 2 4 6 8 10 12 13 14 Time/s The gradient of the line is 2 m s-2 Or: a = (u – v)/t = (20 – 10)/(10 – 0) = 2 m s-2 Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
22. 22. 2.3 Speed-Time Graphs Non-uniform acceleration In a speed-time graph, a curved line denotes non-uniform acceleration. How can you achieve non-uniform acceleration when playing a racing game in an arcade? Answer: by stepping on the pedal slowly to its maximum (increasing acceleration) or by slowly releasing the pedal from its maximum position (decreasing acceleration). Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
23. 23. 2.3 Speed-Time Graphs Non-uniform acceleration Speed/m s-1 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 Time/s The gradient of the speed-time graph is not constant during the first 10 seconds i.e. acceleration is non-uniform. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
24. 24. 2.3 Speed-Time Graphs Types of acceleration Can you tell the difference between the following types of acceleration? Can you sketch the v-t graphs and give an example of each type of acceleration? Positive acceleration Negative acceleration Retardation Increasing acceleration Increasing deceleration Deceleration Decreasing acceleration Decreasing deceleration Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
25. 25. 2.3 Speed-Time Graphs Area under speed-time graph Distance is normally given by speed  time. The area under a speed-time graph is also equal to speed  time. Hence, the area under a speed-time graph gives the distance travelled. The next slide shows you how to find the distance travelled by using the area under the speed-time graph. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
26. 26. 2.3 Speed-Time Graphs Speed/m s-1 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 Time/s From t = 7.5 to t = 12, Speed decreases uniformly, acceleration = (0 - 45)/(12 - 7.5) = -1 m s-1 Distance moved = area of green triangle = 0.5  36  (12 - 7.5) = 81 m Can you find the total distance moved (from t = 0 to t = 12)? Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
27. 27. 2.3 Speed-Time Graphs Key Ideas • A speed-time graph shows how speed changes with time. • The gradient of the tangent at a point on the speed-time graph gives the instantaneous acceleration. • The area under the speed-time graph is the total distance travelled. Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
28. 28. 2.3 Speed-Time Graphs Test Yourself 2.3 1. The figure below shows the speed-time graph of a car. Describe the motions of the car at regions A, B, C and D. 2. The figure below shows the distance-time graph of a car. Describe the motions of the car at regions A, B, C and D. Di stan ce Sp eed D B D C B C A A Ti me Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. Ti me 4 February 2014
29. 29. 2.4 Acceleration of Free Fall In this section, you’ll be able to: • state that the acceleration of free fall near to Earth is approximately 10 m s-2 • describe motion of bodies in free fall with and without air resistance • understand what terminal velocity is Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
30. 30. 2.4 Acceleration of Free Fall Galileo’s Discovery Galileo Galilei, an Italian, was one of the first modern scientists to verify experimentally the acceleration due to free fall. Supposedly experimenting from the Leaning Tower of Pisa, he found out that this ‘falling’ acceleration was about 10 m s-2 and the same for all objects! Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
31. 31. 2.4 Acceleration of Free Fall Falling without air resistance Take a coin from your wallet and hold it in one hand. Hold your wallet in the other hand and stand on your chair. Drop both items from the same height at the same time. What happens? a) The light coin hits the ground first b) The heavy wallet hits the ground first c) Both hit the ground at the same time Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
32. 32. 2.4 Acceleration of Free Fall Falling with air resistance Objects falling without (or with negligible) air resistance fall with 10 m s-2. If air resistance is present, objects will fall with a constant speed. Air resistance: 1. 2. 3. 4. Opposes the motion of moving objects Increases with the speed of the object Increases with surface area Increases with density of air Do you know which skydiver falls faster? Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
33. 33. 2.4 Acceleration of Free Fall Key Ideas • When air resistance is absent, all objects fall under gravity with constant acceleration, g, the acceleration of free fall (about 10 m s-2) • When air resistance is present, all objects falling under gravity experience decreasing acceleration until terminal velocity is reached. (At this point, air resistance equals the weight of the object.) Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. 4 February 2014
34. 34. 2.4 Acceleration of Free Fall Test Yourself 2.4 A parachutist jumps from an aircraft and falls through the air. After some time the parachute opens. Describe the motion of the parachutist at points A, B, C and D. D 50 40 C Speed/m s–1 30 20 B 10 0 A 2 4 6 8 10 12 14 16 18 Copyright © 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd. Time/s 4 February 2014