Applied Mechanics

1. Chapter No.6 Linear Motion Page 1
QUESTIONS
CHAPTER 3 Linear Motion
Type I Problems:
A)
Q.1) A body is moving with a velocity of 2 m/s. After 4 sec the velocity of the body becomes
5 m/s. Find the acceleration of the body.
Q. 2) A car is moving with a velocity of 15 m/s. The car is brought to rest by applying breaks in
5 sec. Determine:
1. The retardation
2. and distance travelled by the car after applying brakes.
B)
Q. 3) A bullet, moving at the rate of 250 m/s, is fired into a log of wood. The bullet penetrates to
a depth of 40 cm. If the bullet is moving with the same velocity is fired into a similar piece of
wood which is 20 cm thick. With what velocity would it emerge? (Take the resistance to be
uniform in both the cases).
Q. 4) A burglar’s car had a start with an acceleration of 2 m/s2
, a police party came after 10 sec
and continued to chase the burglar’s car with a uniform velocity of 40 m/s. Find the time taken,
in which the police van will overtake the car.
Q. 5) A motorist rushing at 30 m/s. Find a child on road 60 m ahead. He instantly stop the engine
and applies brakes so as to stop the car within 20 m of child. Calculate
a) The retardation
b) And the time required stopping the car.
(Assume that brakes produce uniform retardation)

2. Chapter No.6 Linear Motion Page 2
Q.6) On a straight road, a smuggler’s car passes a police station with a uniform velocity of 10
m/s. After 10 sec, a police party follows in pursuit in a jeep with a uniform acceleration of 1
m/s2
. Find the time necessary for the jeep to catch up with a smuggler’s car.
May 2007 (12 mks)
Q.7) An automobile A starting from rest accelerates at a constant rate of 1 m/s2
. Two second
later automobile B start’s from the same position and accelerates at a constant rate of 1.3 m/s2
.
Determine:
a) When and where will B overtake the A and
b) The speed of each automobile at that time.
Jan 2001 (12 mks)
Q. 8) Two car’s are travelling towards each other on a single lane road at the velocities 12 m/s
and 9 m/s respectively. When 100 m apart, both drivers realize the situation and apply their
brakes. They succeed in stooping simultaneously and just short of colliding. Assuming constant
deceleration for each case, determine:
1) The time required for the cars to stop
2) Deceleration for each car
3) The distance travelled by each car while slowing down.
May 2004 (10 Mks)
Type II Problems: FREELY FALLING BODY
1) A stone is dropped into a well is heard to strike a water in 5 sec. Find the depth of well,
assuming velocity of sound 331 m/s.
Dec 2007 (12 mks)
2) A body, is falling under the force of gravity from the top of the tower which covers
(5/9)th
height of tower in last second of its motion. Find the height of the tower.
3) A stone is dropped from the top of tower. During the last second of its flight it is found to
fall (1/4)th
of the whole height of the tower. Find the height of the tower. What is the
velocity with which the stone hits the ground?

3. Chapter No.6 Linear Motion Page 3
4) A tower is 90 m height. A particle dropped from the top of the tower and at the same time
another particle is projected upward from the foot of the foot of the tower. Both the
particle meet at a height of 30 m. Find the velocity, with which the second particle is
projected upward.
5) A tower is 100 m height. A particle dropped from the top of the tower and at the same
time another particle is projected upward from the foot of the foot of the tower. Both the
particle meet at a height of 40 m. Find the velocity, with which the second particle is
projected upward.
6) A stone is dropped from the top of the tower 60 m high. Another stone is projected
upwards at the same time from the foot of the tower and meets the first stone at the height
of 18 m. Find the velocity with which the second stone is projected upward.
7) A stone is dropped from the height. After falling 5 sec from rest, the stone brakes the
glass pan, and in braking the stone loses 20 % of its velocity. Find the distance travelled
by the stone in the next second. Take g = 9.81 m/s2
.
8) A ball is dropped from the top of the tower 30 m high. At the same instant a second ball
is thrown upward from the ground with an initial velocity of 12 m/s. when and where do
they cross with what relative velocity?
Dec 2005 (11 Mks)
9) A ball is thrown vertically upward with an initial velocity of 36 m/s. After 2 secs, another
ball is thrown upwards. What should be the initial velocity so that it crosses the first ball
at a height of 30 m?
Hint: Ball A: ua = 36 m/s, h = 30 m (common for both the balls), time = (t+2)
Ball B: ub = ?, h = 30 m, time = t secs
Using s = ut +
1
2
at2
for ball A and B
First calculate t and then use calculated t for computing the ub.
Type III Problems:
1) Three electric poles A, B and C are erected by the side of straight road. Distance between
two successive pole is 100 m. A car starting from rest and accelerating uniformly passes
the pole A and takes 10 sec to reach pole B and further 8 sec to reach pole C. Calculate

4. Chapter No.6 Linear Motion Page 4
1) The magnitude of acceleration of the car
2) Velocity of the car at poles A, B and C
3) Distance of pole A from the starting point.
Dec 2007 (12 mks)
2) Three marks A, B and C are erected by the side of straight road. Distance between two
successive pole is 150 m. A car starting from rest and accelerating uniformly passes the
pole A and takes 10 sec to reach pole B and further 8 sec to reach pole C. Calculate
4) The magnitude of acceleration of the car
5) Velocity of the car at poles A, B and C
6) Distance of pole A from the starting point.
Type IV Problems:
1) A car starts from rest with a constant acceleration of 4 m/s2
. Determine the distance
travelled in 7th
second
2) A body is moving with uniform acceleration and covers a distance of 15 m in fifth second
and 25 m in 10th
second. Determine:
1) The initial velocity of the body and
2) Acceleration of the body
Type V Problems: Problems on Motion with variable Acceleration
1) The speed of the body moving in a straight line is given by the relation v = 1.25t + (t2/10)
where, v is in m/s and t in sec. Determine the max. accn
, distance travelled from rest in 10
sec.
Dec 1985 (10 Mks)
2) A particle moves along a straight line so that its displacement in meter from a fixed point
is given by,
S = t3+3t2+4t+5
Find:
a) Velocity at start and after 4 second
b) Acceleration at start after 4 second
3) The equation of motion a particle moving in straight line is given by
S = 18t+3t2-2t3
Where s is the distance covered from the starting point in meter at the end of t seconds.

5. Chapter No.6 Linear Motion Page 5
Find:
a) The velocity and acceleration at the start
b) The time, when the particle reaches its max. velocity and
c) The max. velocity of the particle
4) Solve the same problem when S = 15t+3t2-t3
5) A particle moves along a straight line with a velocity given by the equation
V = 2t3-t2-2t+4
Where v is the velocity in m/s and time t in sec. When t = 2 sec, the particle is found to be
at a distance of 10 m from the station A. Determine:
1) The accn
and
2) Displacement of the particle after 6 sec.
6) The equation of motion a particle moving in straight line is given by
S = 16t+4t2-3t3
Where s is in meter and t in seconds.
Find:
a) Displacement, velocity and acceleration 2 sec after start
b) Displacement and acceleration when velocity is zero; and
c) Displacement and velocity when acceleration is zero
Hint: take derivative of s w.r.t. t you will get v
Again take the derivative of calculated v you will get a
Type VI Problems: Problems on Graphs
1) If a body falling freely under the gravity draw the a-t, v-t and s-t diagrams
(May 2009 5 Mks)