CHAPTER 17 ACCELERATION
EXERCISE 70, Page 171
1. A coach increases velocity from 4 km/h to 40 km/h at an average acceleration of 0.2 m/s 2 . Find
the time taken for this increase in velocity.
Average acceleration, a =
vu
t
from which, time taken for increase in velocity, t =
v  u (40  4)km / h

a
0.2 m / s 2
1000 m / km
60  60s / h
0.2 m / s 2
36 km / h 
=
36
m/s
3.6
=
= 50 s
0.2 m / s 2
2. A ship changes velocity from 15 km/h to 20 km/h in 25 min. Determine the average acceleration
in m/s 2 of the ship during this time.
vu
Average acceleration, a =

t
 20  15 m / s
3.6
(25  60) s
= 9.26  104 m / s 2
3. A cyclist travelling at 15 km/h changes velocity uniformly to 20 km/h in 1 min, maintains this
velocity for 5 min and then comes to rest uniformly during the next 15 s. Draw a velocity/time
graph and hence determine the accelerations in m/s 2 (a) during the first minute, (b) for the next
5 minutes, and (c) for the last 10 s.
The velocity/time graph is shown below.
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v  u  20  15  km / h
(a) Average acceleration, a =


t
60s
 20  15 m / s
3.6
1min
5
m/s
 3.6
= 0.0231m / s 2
60s
(b) Since the speed does not change then the average acceleration is zero
v  u  0  13.33 km / h


(c) Average acceleration, a =
t
10s
 13.33 m / s
3.6
10s
=  0.370m / s 2
4. Assuming uniform accelerations between points draw the velocity/time graph for the data given
below, and hence determine the accelerations from A to B, B to C and C to D:
Point
A
B
C
D
Speed (m/s)
25
5
30
15
Time (s)
15
25
35
45
The velocity/time graph is shown below.
Acceleration from A to B =
change in velocity  5  25  m / s

= - 2 m / s2
time taken
25

15
s


Acceleration from B to C =
change in velocity  30  5  m / s 25

 m / s 2 = 2.5 m / s 2
time taken
 35  25 s 10
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© John Bird Published by Taylor and Francis
Acceleration from C to D =
change in velocity 15  30  m / s 15


m / s 2 = - 1.5 m / s 2
time taken
10
 45  35 s
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© John Bird Published by Taylor and Francis
EXERCISE 71, Page 173
1. An object is dropped from the third floor of a building. Find its approximate velocity 1.25 s later
if all forces except that of gravity are neglected.
Velocity after 1.25 s, v = u + at = 0 + (9.8)(1.25) = 12.25 m/s
2. During free fall, a ball is dropped from point A and is travelling at 100 m/s when it passes point
B. Calculate the time for the ball to travel from A to B if all forces except that of gravity are
neglected
Velocity, v = u + at
i.e.
100 = 0 + 9.8(t)
from which, time to travel from A to B, t =
100 m / s
= 10.2 s
9.8 m / s 2
3. A piston moves at 10 m/s at the centre of its motion and decelerates uniformly at 0.8 m/s 2 .
Determine its velocity 3 s after passing the centre of its motion.
Velocity after 3 s, v = u + at = 10 + (- 0.8)(3) = 7.6 m/s
4. The final velocity of a train after applying its brakes for 1.2 min is 24 km/h. If its uniform
retardation is 0.06 m/s 2 , find its velocity before the brakes are applied.
Velocity of train, v = u + at
Hence,
i.e.
24
= u + (- 0.06)(1.2 × 60)
3.6
6.6 6 = u – 4.32
from which, final velocity, u = 6.666 + 4.32 = 10.98 6 m/s
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© John Bird Published by Taylor and Francis
= 10.98 6 × 3.6 km/h = 39.6 km/h
5. A plane in level flight at 400 km/h starts to descend at a uniform acceleration of 0.6 m/s 2 . It
levels off when its velocity is 670 km/h. Calculate the time during which it is losing height.
Velocity of plane, v = u + at
Hence,
670 400
=
+ (0.6)(t)
3.6
3.6
 670 400 


m / s
3.6 3.6 

from which, time during which it is losing height, t =
= 125 s = 2 min 5 s
0.6 m / s 2
6. A lift accelerates from rest uniformly at 0.9 m/s 2 for 1.5 s, travels at constant velocity for 7 s and
then comes to rest in 3 s. Determine its velocity when travelling at constant speed and its
acceleration during the final 3 s of its travel.
Velocity, v = u + at from which, acceleration, a =
i.e.
vu
t
0.9 =
v0
1.5
from which, velocity at constant speed, v = (0.9)(1.5) = 1.35 m/s
and
acceleration, a =
v  u 0  1.35

= - 0.45 m / s 2
t
3
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© John Bird Published by Taylor and Francis
EXERCISE 72, Page 173
Answers found from within the text of the chapter, pages 169 to 173.
EXERCISE 73, Page 173
1. (b) 2. (a) 3. (c) 4. (e) 5. (i) 6. (g) 7. (d) 8. (c) 9. (a) 10. (d)
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