1. ppr maths nbk
CHAPTER 6 : DISTANCE AND AREA UNDER A GRAPH
NOTES :
1. Distance-Time graph
Distance
uniform
speed
stationary
y
x
Time
0
a) Speed = Gradient of a distance- time graph
= Change of distance = y
Change of time x
b) Average speed = Total distance travelled
Total time taken
2. Speed - Time Graph
Speed
constant speed
acceleration
Area = Total distasnce deceleration
travelled
Time
0
a) Acceleration or deceleration(Rate of change of speed) = Gradient of a speed- time
graph
= Change in speed
Change in time
b) Total distance travelled = Area under the speed –time graph

2. ppr maths nbk
Exercise 1
1. Distance (m)
700
500
0 10 15 30 Time (s)
The diagram shows the distance-time graph of a particle for a period of 30 s. State the
length of time in which the particle is stationary.
Answer:
2. Distance (m)
Q
30
P
5
0 4 Time (s)
The diagram shows the distance-time graph of a particle for a period of 4 s. Find the
distance from P to Q.
Answer:

3. ppr maths nbk
3.
Distance (m)
160
0 2 3 6
Time (hours)
The distance-time graph above shows the journey of a van over a period of 6 hours. Find
the speed, in km h-1, of the van in the first 2 hours.
Answer:
4.
Distance (km)
100
60
0 1 1.5 2 4 Time (hours)
The distance-time graph above illustrates the journey of a car over a period of 4 hours.
Find the average speed, in km h-1, of the car for the whole journey.
Answer:

4. ppr maths nbk
5.
Distance (km)
36 Q
20
P
0 15 40 Time (minutes)
The diagram shows the distance-time graph of a particle for a period of 40 minutes. Find
the average speed from P to Q.
Answer:
6. Speed (ms-1)
12
8
5 9 Time (s)
0
The diagram shows the speed-time graph of a particle for a period of 9 seconds. Find the
length of time at constant speed.
Answer:

5. ppr maths nbk
7. Speed (ms-1)
20
0 3 7 Time (s)
The diagram shows the speed-time graph of a particle for a period of 7 seconds. Find the
rate of change of speed in the last 4 s.
Answer:
8.
Speed (ms-1)
10
0 4 9 Time (s)
The diagram shows the speed-time graph of a particle for a period of 9 seconds. Find the
distance travelled in the last 5 s.
Answer:

6. ppr maths nbk
9.
Speed (ms-1)
16
0 5 7 10 Time (s)
The diagram shows the speed-time graph of a particle for a period of 10 seconds. Find the
total distance travelled in the first 7 s.
Answer:
10.
Speed (ms-1)
18
13
4
3 7 10 Time (s)
0
The diagram shows the speed-time graph of a particle for a period of 10 seconds. Find the
rate of change of speed in the last 3 s.
Answer:

7. ppr maths nbk
Exercise 2
1. Distance (km)
200 R
Q
125
P
2 5 Time (h)
0
The figure shows the distance-time graph of Mr. Tan’s journey from town P to town Q
and then to town R.
Calculate
a) the speed from town P to b) the speed from town Q to c) the average speed for the
town Q, town R, whole journey.
2. Distance (km)
P
80
Q R
50
S
1000 1100 1200 1430 Time
The figure shows the distance-time graph of an object travelling from town P to town S.
Calculate
a) the speed from P to Q, b) the speed from Q to R, c) the speed from R to S.

8. ppr maths nbk
3.
Speed (ms-1)
100
24
6 10 Time (s)
0
The figure shows the speed-time graph of an object during a period of 10 seconds.
Calculate
a) the speed of the object when t = 3 b) the distance travelled in the first 10
seconds.
4. Speed (ms-1)
9
10 30 70 Time (s)
0
The figure shows the speed-time graph of an object for a particular journey.
Calculate
a) the acceleration during the first 10 b) the total distance travelled for the whole
seconds, journey.

9. ppr maths nbk
5.
Speed (ms-1)
bus
6
bicycle
4
0 30 70 90 Time (s)
The figure shows the speed-time graph of a bicycle and a bus during a period of 90
seconds.
Calculate
a) the distance travelled by the bicycle b) the distance travelled by the bus during
during the 90 seconds, the 90 seconds.
6.
Distance (m)
70
40
0 2 5 9 12 Time (s)
The figure shows the distance-time graph of a particle over a period of 12 seconds.
Calculate
a) the speed of the particle, from 5 b) the average speed of the particle, for the
seconds to 9 seconds, whole journey.

10. ppr maths nbk
7.
Distance (m)
y
4
0 14 Time (s)
6
The figure shows the distance-time graph of an object over a period of 14 seconds .The
speed of the object during the first 6 seconds is 3 ms-1.
Calculate
a) the value of y, b) the average speed of the object for the
whole journey.
8.
Speed(m s-1 )
12
0 4 10 Time (s)
The figure shows the speed-time graph of a particle for a period of 10 seconds. Calculate
the rate of change of speed, in m s-2, during the first 4 seconds.
Answer:

11. ppr maths nbk
9.
Speed (m s-1)
20
12
4 Time (s)
0 t
The figure shows the speed-time graph of a particle during a period of t seconds
a) Calculate the rate of change of speed b) Given that the total distance travelled in
during the first 4 seconds. the t seconds is 124m, find the value of
t.
10.
Speed (ms-1)
15
9
Time (s)
0 20 65 90
The figure shows the speed-time graph of a train over a period of 90 seconds.
Calculate
a) the deceleration of the train during the b) the total distance travelled during the 90
first 20 seconds, seconds.

12. ppr maths nbk
Diagnostic Test
Distance(m)
1.
12
u
Time (s)
0 3 8
The diagram shows a distance- time graph of an object over a period of 8 seconds.
Given that its uniform speed in the first 3 seconds is 2 ms −1 , calculate
(a) the value of u,
(b) the distance travelled in the last 5 seconds.
(c) its average speed during the 8 seconds.
Speed (ms −1 )
2.
u
16
0 4 12 20 Time (s)
The diagram shows the speed-time graph of an object over a period of 20
seconds.
Calculate
(a) the rate of change of speed in the first 4 seconds,
(b) the value of u, if the distance travelled in the last 8 seconds is 160m.

13. ppr maths nbk
3. Speed (ms −1 )
12
u
Time(s)
0 5 15
The diagram shows a speed –time graph of an object over a period of 15 seconds.
Calculate
(a) the distance travelled at uniform speed,
(b) the value of u, if its average speed during the first 15 seconds is 11 ms −1
]
4. Speed (ms −1 )
20
5
0 16 t Time (s)
The diagram shows speed-time graph of an object over a period of t seconds.
Given that the total distance travelled by the object during the t seconds is 115 meter,
calculate
(a) the distanvce travelled from the 16th seconds to the t-seconds,
(b) the value of t.

14. ppr maths nbk
5. Speed (ms −1 )
v
2
0 4 10 Time (s)
The diagram shows the speed-time graph of an object over a period of 10 seconds.
Calculate the value of v for each situations below :
(a) if the rate of change of speed during the first 4 seconds is -3 ms −2 .
(b) if the total distance travelled during the 10 seconds is 28 meter.

15. ppr maths nbk
CHAPTER 6 : GRADIENT AND AREA UNDER A GRAPH
Answers
Exercise 1
1. 5s
2. 25 m
3. 80
4. 50
5. 0.9 km / min
6. 5s
7. -5 ms-2
8. 50 m
9. 72 m
5
10. ms-2
3
Exercise 2
1a) 62.5 kmh-1 b) 25 kmh-1 c) 40 kmh-1
2a) 30 kmh-1 b) 0 kmh-1 c) 20 kmh-1
3a) 62 b) 468 m
4a) 0.9 ms-2 b) 405 m
5a) 360m b) 390 m
2
6a) 7.5 ms-1 b) 11 ms-1
3
6
7a) 22 b) 2 ms-1
7
8) 3
9a) 2 m s-2 b) 7
10a) 0.3 ms-2 b) 945m
Diagnostic Test
1. (a) 6
(b) 6
(c) 1.5
2. (a) 4
(b) 40
3. (a) 120
(b) 6
4. (a) 75
(b) 22
5. (a) 14
(b) 9