Unit 2

PHYSICS Matters for GCE ‘O’ Level
Unit 2: Kinematics

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

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)


4 February 2014

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


4 February 2014

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


4 February 2014

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.


4 February 2014

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


4 February 2014

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

4 February 2014

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

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

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


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

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


16

18

20

Time/s
4 February 2014

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.


4 February 2014

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


4 February 2014

2.2 Speed, Velocity and Acceleration
• state what velocity and uniform acceleration are
change in velocity
• calculate acceleration using
Time taken
• interpret given examples of non-uniform acceleration


4 February 2014

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?


travelled
200 m

4 February 2014

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?


4 February 2014

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.


4 February 2014

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?

4 February 2014

2.3 Speed-Time Graphs
• plot and interpret speed-time graphs
• determine the distance travelled by calculating the area
under the speed-time graph


4 February 2014

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.


4 February 2014

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

4 February 2014

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).


4 February 2014

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.

4 February 2014

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


4 February 2014

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.


4 February 2014

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)?

4 February 2014

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.


4 February 2014

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


Ti me

4 February 2014

2.4 Acceleration of Free Fall
• 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


4 February 2014

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!


4 February 2014

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


4 February 2014

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?


4 February 2014

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.)


4 February 2014

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


Time/s
4 February 2014

Unit 2

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