1. 1 5.1 Speed, velocity and acceleration Chapter 5A Speed How can we describe how fast an object moves? E.g.A car on a highway travels 90 km in 1 hour. We say that the car travels at a speed of 90 km h –1.

2. 2 5.1 Speed, velocity and acceleration 1Speed Speed is a measure of how fast something moves. Speed = distance travelled per unit of time SI unit: m s –1 or km h –1 (for long distances) An object does not always move at the same speed.

3. 3 5.1 Speed, velocity and acceleration and speeds up again to 60 km h –1. aAverage speed (refer to p.1, notes [chapter 5A]) Its average speed over the whole trip overall distance travelled total time of travel slows down to 0 km h –1, For example, A car travels at 50 km h –1, For example, A car travels at 50 km h –1, 1Speed = = d t

4. 4 5.1 Speed, velocity and acceleration Average speed Classwork 1 (refer to Classwork [Chapter 5A]) Griffith Joyner is the world record holder of ladies 100-metre race. She could run 100 m in 10.49 s. What was her average speed? Average speed = 100 m 10.49 s = ms -1 = kmh -1 = 9.53 34.3 9.53 × 3.6

5. 5 5.1 Speed, velocity and acceleration Average speed Classwork 2 The speed limit on Tuen Mun Highway is 70 kmh -1. To detect speeding, police set up two photo-detectors 80 m apart on the road side. A car drove past the two detectors. Would the driver be prosecuted for speeding?

6. 6 5.1 Speed, velocity and acceleration Average speed Average speed = Photo- detectors m s =______ms -1 = __________kmh -1 = _____ kmh -1 Therefore, the driver will be ____________ prosecuted 80 2.85 28 28 × 3.6 101

7. 7 5.1 Speed, velocity and acceleration Average speed does not tell the variations during the trip. On most trips, the speed at any instant is often different from the average speed. aAverage speed 1Speed Note:

8. 8 5.1 Speed, velocity and acceleration bInstantaneous speed ( 瞬時速率 ) = speed at any instant E Instantaneous speed 1Speed The word ‘speed’ alone  instantaneous speed Instantaneous speed  distance travelled in an extremely short time interval

9. 9 5.1 Speed, velocity and acceleration Speedometer tells the car’s speed at any instant! 1Speed bInstantaneous speed E

10. 10 5.1 Speed, velocity and acceleration Instantaneous speed ( 瞬時速率 ) [p.2, Classwork] Can be estimated by measuring the distance traveled in a very short time interval. Measuring instantaneous speed with a timer-scaler.

11. 11 5.1 Speed, velocity and acceleration Average speed of the trolley as it passes the detector = width of card / time interval Classwork 3 A trolley has a card of width 3 cm attached to it. It runs down an inclined runway passing a light detector which is connected to a timer- scaler. The timer-scaler records a time of 40ms. Calculate the speed of the trolley as it passes the light detector. Since the time interval is very small, the average speed can be taken as the instantaneous speed at the mid-point of the time interval.

12. 12 5.1 Speed, velocity and acceleration Solution (Classwork 3) Width of card = 3 cm =______________m Time interval = 40 ms = ______________s Average speed of trolley as it passes the light detector = __________________= ________________ms -1 Since the time interval is very __________, the average speed may be taken as the _______________________ of the trolley at the __________________ of the time interval. 0.03 0.04 0.03/0.04 ms -1 0.75 short instantaneous speed mid-point (at 0.02s)

13. 13 5.1 Speed, velocity and acceleration 2Velocity -see p.1, notes(chapter 5A) rate of change of displacement. a speed in a given direction or velocity a vector quantity direction magnitude (speed) Velocity is...

14. 14 5.1 Speed, velocity and acceleration speed = 300 km h –1 direction = west MTR drivers concern speed only. aSpeed with direction 2Velocity Pilots concern velocity (direction & speed). speed = 90 km h –1

15. 15 5.1 Speed, velocity and acceleration bAverage velocity Average velocity = overall displacement total time of travel direction of velocity = direction of overall displacement 2Velocity = s t

16. 16 5.1 Speed, velocity and acceleration 2Velocity A car on a circular track may have a constant speed, but it does not have a contant velocity. It’s velocity changes as its direction changes. Remarks: (p.3, notes (chapter 5A)) 1.The magnitude of it’s speed has the same value to the magnitude of it’s velocity. 2.The car keeps changing its direction. Therefore, its velocity is changing.

17. 17 5.1 Speed, velocity and acceleration Example 1 A boy walks along a curve PQR, which is made up of two semi-circular parts PQ and QR of radius 6 m and 4 m respectively. He take 5 s to walk from P to Q and 2 s from Q to R

18. 18 5.1 Speed, velocity and acceleration Constant Velocity When an object is moving at a constant speed along a straight line (fixed direction), it is said to have a constant velocity.

19. 19 5.1 Speed, velocity and acceleration Average speed and velocity Question ? Example 3 e.g. 3

20. 20 5.1 Speed, velocity and acceleration 1The world record of women…The world record of women… 2In an orienteering event, Maria and…In an orienteering event, Maria and… 3True or false: The average…True or false: The average… 4True or false: A man takes a walk…True or false: A man takes a walk… Check-point 1 E

21. 21 5.1 Speed, velocity and acceleration Q1The world record... ( ) Average speed = 10.49 = 9.53 m s –1 or 34.3 km h –1 100 The world record of women 100-m race is 10.49 s. What is the average speed?

22. 22 5.1 Speed, velocity and acceleration In an orienteering event, Maria and Karen reach their control points at the same time. Q2In an orienteering event... start, 10:00 am Maria, 10:30 am Karen, 10:30 am Who runs in a higher average velocity?

23. 23 5.1 Speed, velocity and acceleration AMaria. BKaren. CUndetermined since their paths are unknown. DIncomparable since they run along different directions. Who runs in a higher average velocity? Q2In an orienteering event...

24. 24 5.1 Speed, velocity and acceleration Note: The distance travelled is equal to magnitude of displacement only if it is a straight-line motion. Speed is usually larger than the magnitude of velocity. Q3True or false: (T/F) Average speed of an object  magnitude of its average velocity.

25. 25 5.1 Speed, velocity and acceleration A man takes a walk starting from rest and ending at rest. Q4True or false: (T/F) It is possible for him to attain an average speed of 5 km h –1 but he never goes faster than 5 km h –1. E

26. 26 5.1 Speed, velocity and acceleration 3Acceleration When a car moves faster and faster, its speed is increasing (velocity changed).

27. 27 5.1 Speed, velocity and acceleration 3Acceleration When a car moves slower and slower, its speed is decreasing (velocity changed).

28. 28 5.1 Speed, velocity and acceleration When a car changes direction, its velocity changes too. 3Acceleration

29. 29 5.1 Speed, velocity and acceleration 3Acceleration Acceleration measures the change in velocity Acceleration =  velocity per unit time direction speed overall change in velocity total time taken = m s –2 Unit: m s –1 / s vector quantity =

30. 30 5.1 Speed, velocity and acceleration If a car accelerates at 2 m s –2, what does that mean? 3Acceleration t = 1 s v = 2 m s –1,  v = 2 m s –1 v = 0 t = 2 s v = 4 m s –1,  v = 2 m s –1 v = 6 m s –1,  v = 2 m s –1 t = 3 s 1 m t = 0 3 m 5 m

31. 31 5.1 Speed, velocity and acceleration Acceleration of Ferrari 348 Question ? Example 4 e.g. 4

32. 32 5.1 Speed, velocity and acceleration 1A running student is slowing down…A running student is slowing down… 2When time is measured in hour (h)…When time is measured in hour (h)… 3In 2.5 s, a car speeds up from…In 2.5 s, a car speeds up from… 4A car is moving in positive direction…A car is moving in positive direction… Check-point 2

33. 33 5.1 Speed, velocity and acceleration Q1A running student... A running student is slowing down in front of a teacher. With reference to the sign convention, Acceleration of student: positive / negative Velocity of student: positive / negative +ve

34. 34 5.1 Speed, velocity and acceleration Quantity Unit Scalar/Vector Speed ______ _____ Velocity ______ _____ Change in velocity ______ _____ Acceleration ______ _____ Q2When time is measured... Unit of time: hour (h) km h –1 km h –2 scalar vector Unit of distance/displacement: kilometer (km)

35. 35 5.1 Speed, velocity and acceleration Q3In 2.5 s, a car speeds up... In 2.5 s, a car speeds up from 60 km h –1 to 65 km h –1... …while a bicycle goes from rest to 5 km h –1. Which one has the greater acceleration? They have the same acceleration!

36. 36 5.1 Speed, velocity and acceleration Q4A car is moving in positive... A car is moving in +ve direction. What happens if it moves under a  ve acceleration? What happens if it moves under a  ve deceleration? The car will slow down. The car will move in +ve direction with increasing speed.

37. 37 5.1 Speed, velocity and acceleration The End

38. 38 5.1 Speed, velocity and acceleration Airport Express takes 0.35 h to go from HK station to Airport station (34 km). Example 1 Average speed of Airport Express HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h –1 2.6 8.9 (a) 153 (b) 762 (c) 90 105  Ave. speed = 34 km/0.35 h Complete table. = 97 km h –1

39. 39 5.1 Speed, velocity and acceleration Example 1 Average speed of Airport Express HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h –1 2.6 8.9 (a) 153 (b) 762 (c) 90 105 (a)Tsing Yi  Airport: Distance = ave. speed  time = 105  12.7 762 s = (762/3600) h = 12.7 h = 22.2 km

40. 40 5.1 Speed, velocity and acceleration Example 1 Average speed of Airport Express HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h –1 2.6 8.9 (a) 153 (b) 762 (c) 90 105 (b)Kln  Tsing Yi: Time = distance / ave. speed = 8.9 / 90 = 0.0989 h = 356 s

41. 41 5.1 Speed, velocity and acceleration Example 1 Average speed of Airport Express HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h –1 2.6 8.9 (a) 153 (b) 762 (c) 90 105 (c)HK  Kln: Ave. speed = distance / time = 2.6 / 0.0425 153 s = (153/3600) h = 0.0425 h = 61.2 km

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43. 43 5.1 Speed, velocity and acceleration A man walks from A to B at 1 km h –1, A B 1 km h –1 Example 2 Average speed of a return trip 2 km h –1 and returns at 2 km h –1. Average speed for the whole trip = ?

44. 44 5.1 Speed, velocity and acceleration = 1.33 km h –1 A B 1 km h –1 2 km h –1 Example 2 Average speed of a return trip Suppose AB = 1 km Time for whole trip = = 1 h + 0.5 h = 1.5 h  whole journey = 2 km Ave. speed = distance / time = 2/1.5

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46. 46 5.1 Speed, velocity and acceleration A car travels 7 km north and then 3 km west in 10 minutes. Find C B A 3 km 7 km Example 3 Average speed and velocity (a) average speed, Ave. speed = distance travelled time taken = (7 + 3) km (10/60) h = 60 km h –1

47. 47 5.1 Speed, velocity and acceleration Example 3 Average speed and velocity A car travels 7 km north and then 3 km west in 10 minutes. Find C B A 3 km 7 km (b) ave. velocity? AC = = 7.62 km  tan  =  =23.2 o 3/7

48. 48 5.1 Speed, velocity and acceleration Example 3 Average speed and velocity A car travels 7 km north and then 3 km west in 10 minutes. Find C B A 3 km 7 km AC = 7.62 km,  =23.2 o  Size of ave. velocity = = 45.7 km h –1 displacement time 7.62 km (10/60) h = Ave. velocity is 45.7 km h –1, 23.2° north of west. (b) ave. velocity?

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50. 50 5.1 Speed, velocity and acceleration The Ferrari 348 can go from rest to 100 km h –1 in 5.6 s. Example 4 Acceleration of Ferrari 348 What is its ave. acceleration (in m s –2 )? Ave. acceleration = 100 km h –1 5.6 s (100/3.6) m s –1 5.6 s = = 4.96 m s –2

51. 51 5.1 Speed, velocity and acceleration Return