1. Speed, velocity and acceleration

2. 1 Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

3. Comment on their their argument.
Who runs faster?
No, I travelled
longer distance every
minute.
Me, as I spent
less time on the
trip.
Comment on their their argument.

4. 2 A boy has been missing in a forest for 2 hours.
radius = 8 km
scale = 1 cm : 5 km O
(a) If he walks at a speed of 4 km h–1,
try to locate his possible positions on the map.

5. 2 A boy has been missing in a forest for 2 hours.
radius = 8 km
scale = 1 cm : 5 km O
(b) What else is important to spot the boy?
The direction in which he has been walking.

6. 1 Speed How can we describe how fast an object moves?
E.g. A car on Tolo Highway travels 90 km in 1 hour.
We say that the car travels at a speed of 90 km h–1.

7. Speed = distance travelled per unit of time
How can we describe how fast an object moves?
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)

8. a Average speed A car travels at 50 km h–1, slows down to 0 km h–1,
and speeds up again to 60 km h–1.
Its average speed over the whole journey
overall distance travelled =
total time of travel

9. 1 Speed
a Average speed
Average speed does not tell the variations during the journey.
On most trips, the speed at any instant is often different from the average speed.

10. b Instantaneous speed = speed at any instant
The word ‘speed’ alone  instantaneous speed
Instantaneous speed
 distance travelled in an extremely short time interval
Simulation

11. Speedometer tells the car’s speed at any instant!
b Instantaneous speed
Speedometer tells the car’s speed at any instant!

12. rate of change of displacement.
2 Velocity
Velocity is...
a speed in a given direction or
rate of change of displacement.
direction
a vector
quantity
velocity
magnitude
(speed)

13. a Speed with direction MTR drivers concern speed only.
2 Velocity
a Speed with direction
MTR drivers concern speed only.
speed = 90 km h–1
Pilots concern velocity (direction & speed).
speed = 300 km h–1
direction = west

14. b Average velocity overall displacement Average velocity =
total time of travel
direction of overall displacement
direction of velocity =

15. c Instantaneous velocity
The velocity at any instant is called instantaneous velocity.
If a car moves at a constant velocity...
… its average and instantaneous velocities have the same value.

16. Q1 The world record...
The world record of women 100-m race is s.
What is the average speed?
( )
Average speed =
10.49
100
= 9.53 m s–1 or 34.3 km h–1

17. Q2 In an orienteering event...
In an orienteering event, Maria and Karen reach their control points at the same time.
start, 10:00 am
Maria, 10:30 am
Karen, 10:30 am
Who runs in a higher average velocity?

18. Q2 In an orienteering event...
Who runs in a higher average velocity?
A Maria.
B Karen.
C Undetermined since their paths are unknown.
D Incomparable since they run along different directions.

19. Q3 True or false:
Average speed of an object  magnitude of its average velocity.
(T/F)
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.

20. Q4 True or false:
A man takes a walk starting from rest and ending at rest.
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.
(T/F)

21. 3 Acceleration When a car moves faster and faster,
its speed is increasing (velocity changed).

22. 3 Acceleration When a car moves slower and slower,
its speed is decreasing (velocity changed).

23. 3 Acceleration
When a car changes direction,
its velocity changes too.

24. 3 Acceleration Acceleration measures the change in velocity direction
speed
Acceleration = velocity per unit time
overall change in velocity =
total time taken
vector quantity
Unit: m s–1 / s
= m s–2

25. 3 Acceleration t = 0 v = 0 t = 1 s v = 2 m s–1, v = 2 m s–1 t = 2 s
If a car accelerates at 2 m s–2, what does that mean?
t = 0
v = 0
t = 1 s
v = 2 m s–1,
v = 2 m s–1
1 m
t = 2 s
v = 4 m s–1,
v = 2 m s–1
3 m
t = 3 s
v = 6 m s–1,
v = 2 m s–1
5 m

26. Example 1
Airport Express takes 0.35 h to go from HK station to Airport station (34 km).
 Ave. speed =
34 km/0.35 h
= 97 km h–1
Complete table.
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

27. Example 1 (b) Kln  Tsing Yi: Time = distance / ave. speed = 8.9 / 90
= h
= 356 s
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

28. Example 1 (a) Tsing Yi  Airport: Distance = ave. speed  time
= 105  12.7
= 22.2 km
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
762 s
= (762/3600) h
= 12.7 h

29. Example 1 (c) HK  Kln: Ave. speed = distance / time = 2.6 / 0.0425
= 61.2 km
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
153 s
= (153/3600) h
= h

30. Example 2 A man walks from A to B at 1 km h–1,
and returns at 2 km h–1.
1 km h–1 A B
2 km h–1
Average speed for the whole trip = ?

31. Ave. speed = distance / time
Example 2
1 km h–1 A B
2 km h–1
Suppose AB = 1 km
 whole journey = 2 km
Time for whole trip =
= 1 h h = 1.5 h
Ave. speed = distance / time
= 2/1.5
= 1.33 km h–1

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

33. Example 3
A car travels 7 km north and then 3 km west in 10 minutes. Find
(b) ave. velocity?
3 km C B
AC =
7 km
= 7.62 km 
tan q =
3/7
 q =23.2o A

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

35. Example 4 The Ferrari 348 can go from rest to 100 km h–1 in 5.6 s.
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

36. Q1 A running student...
A running student is slowing down in front of a teacher.
+ve
With reference to the sign convention,
Velocity of student: positive / negative
Acceleration of student: positive / negative

37. Q2 When time is measured... Unit of time: hour (h)
Unit of distance/displacement: kilometer (km)
Quantity Unit Scalar/Vector
Speed ______ _____
Velocity ______ _____
Change in velocity ______ _____
Acceleration ______ _____
km h–1
scalar
km h–1
vector
km h–1
vector
km h–2
vector

38. They have the same acceleration!
Q3 In 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!

39. Q4 A car is moving in positive...
A car is moving in +ve direction.
What happens if it moves under a ve acceleration?
The car will slow down.
What happens if it moves under a ve deceleration?
The car will move in +ve direction with increasing speed.