Motion in a Straight Line Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. The co-ordinates of a moving particle at any time ‘t’are given by x =
at
3
  and y = ßt
3
. The speed of the particle at  time ‘t’ is given by
(a)
(b)
(c)
(d)
2. A goods train accelerating uniformly on a straight railway track,
approaches an electric pole standing on the side of track. Its engine
passes the pole with velocity u and the guard’s room passes with
velocity v. The middle wagon of the train passes the pole with a
velocity
(a)
Page 2


PART-I (Single Correct MCQs)
1. The co-ordinates of a moving particle at any time ‘t’are given by x =
at
3
  and y = ßt
3
. The speed of the particle at  time ‘t’ is given by
(a)
(b)
(c)
(d)
2. A goods train accelerating uniformly on a straight railway track,
approaches an electric pole standing on the side of track. Its engine
passes the pole with velocity u and the guard’s room passes with
velocity v. The middle wagon of the train passes the pole with a
velocity
(a)
(b)
(c)
(d)
3. A particle starts moving rectilinearly at time t = 0 such that its velocity
v changes with time t according to the equation v = t
2
 – t where t is in
seconds and v is in m/s. Find the time interval for which the particle
retards.
(a) < t < 1
(b) > t > 1
(c) < t < 1
(d) < t < 
4. A ball is dropped on a floor and bounces back to a height somewhat less
than the original height. Which of the curves depicts its motion
correctly?
(a)
(b)
Page 3


PART-I (Single Correct MCQs)
1. The co-ordinates of a moving particle at any time ‘t’are given by x =
at
3
  and y = ßt
3
. The speed of the particle at  time ‘t’ is given by
(a)
(b)
(c)
(d)
2. A goods train accelerating uniformly on a straight railway track,
approaches an electric pole standing on the side of track. Its engine
passes the pole with velocity u and the guard’s room passes with
velocity v. The middle wagon of the train passes the pole with a
velocity
(a)
(b)
(c)
(d)
3. A particle starts moving rectilinearly at time t = 0 such that its velocity
v changes with time t according to the equation v = t
2
 – t where t is in
seconds and v is in m/s. Find the time interval for which the particle
retards.
(a) < t < 1
(b) > t > 1
(c) < t < 1
(d) < t < 
4. A ball is dropped on a floor and bounces back to a height somewhat less
than the original height. Which of the curves depicts its motion
correctly?
(a)
(b)
(c)
(d)
5. The displacement x of a particle varies with time according to the
relation  Then select the false alternative.
(a) At , the displacement of the particle is nearly 
(b) The velocity and acceleration of the particle at t = 0 are a and –ab
respectively
(c) The particle cannot go beyond
(d) The particle will not come back to its starting point at t ? 8
6. The deceleration experienced by a moving motor boat after its engine is
cut off, is given by dv/dt = – kv
3
 where k is a constant. If v
0
 is the
magnitude of the velocity at cut-off, the magnitude of the velocity at a
time t after the cut-off is
(a)
(b) v
0 
e
–kt
(c) v
0 
/ 2
(d) v
0
7. A car, starting from rest, accelerates at the rate f through a distance S,
then continues at constant speed for time t and then decelerates at the
Page 4


PART-I (Single Correct MCQs)
1. The co-ordinates of a moving particle at any time ‘t’are given by x =
at
3
  and y = ßt
3
. The speed of the particle at  time ‘t’ is given by
(a)
(b)
(c)
(d)
2. A goods train accelerating uniformly on a straight railway track,
approaches an electric pole standing on the side of track. Its engine
passes the pole with velocity u and the guard’s room passes with
velocity v. The middle wagon of the train passes the pole with a
velocity
(a)
(b)
(c)
(d)
3. A particle starts moving rectilinearly at time t = 0 such that its velocity
v changes with time t according to the equation v = t
2
 – t where t is in
seconds and v is in m/s. Find the time interval for which the particle
retards.
(a) < t < 1
(b) > t > 1
(c) < t < 1
(d) < t < 
4. A ball is dropped on a floor and bounces back to a height somewhat less
than the original height. Which of the curves depicts its motion
correctly?
(a)
(b)
(c)
(d)
5. The displacement x of a particle varies with time according to the
relation  Then select the false alternative.
(a) At , the displacement of the particle is nearly 
(b) The velocity and acceleration of the particle at t = 0 are a and –ab
respectively
(c) The particle cannot go beyond
(d) The particle will not come back to its starting point at t ? 8
6. The deceleration experienced by a moving motor boat after its engine is
cut off, is given by dv/dt = – kv
3
 where k is a constant. If v
0
 is the
magnitude of the velocity at cut-off, the magnitude of the velocity at a
time t after the cut-off is
(a)
(b) v
0 
e
–kt
(c) v
0 
/ 2
(d) v
0
7. A car, starting from rest, accelerates at the rate f through a distance S,
then continues at constant speed for time t and then decelerates at the
rate  to come to rest. If the total distance traversed is 15 S , then
(a) S = 
(b) S = f t
(c) S = 
(d) S = 
8. A stone falls freely  under gravity. It covers distances h
1
, h
2
 and h
3
 in
the first 5 seconds, the next 5 seconds and the next 5 seconds
respectively. The relation between h
1
, h
2
 and h
3
 is
(a) h
1
 =  = 
(b) h
2
 = 3h
1
 and h
3
 = 3h
2
(c) h
1
 = h
2
 = h
3
(d) h
1
 = 2h
2
 = 3h
3
9. Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0
in the same direction along a straight line. The velocity time graph of
two cars is shown in figure. The time when the car B will catch the car
A, will be
(a) t = 21 sec.
(b) t = 
(c) t =  20 sec.
(d) None of these
10. A body starts from rest and travels a distance x with uniform
Page 5


PART-I (Single Correct MCQs)
1. The co-ordinates of a moving particle at any time ‘t’are given by x =
at
3
  and y = ßt
3
. The speed of the particle at  time ‘t’ is given by
(a)
(b)
(c)
(d)
2. A goods train accelerating uniformly on a straight railway track,
approaches an electric pole standing on the side of track. Its engine
passes the pole with velocity u and the guard’s room passes with
velocity v. The middle wagon of the train passes the pole with a
velocity
(a)
(b)
(c)
(d)
3. A particle starts moving rectilinearly at time t = 0 such that its velocity
v changes with time t according to the equation v = t
2
 – t where t is in
seconds and v is in m/s. Find the time interval for which the particle
retards.
(a) < t < 1
(b) > t > 1
(c) < t < 1
(d) < t < 
4. A ball is dropped on a floor and bounces back to a height somewhat less
than the original height. Which of the curves depicts its motion
correctly?
(a)
(b)
(c)
(d)
5. The displacement x of a particle varies with time according to the
relation  Then select the false alternative.
(a) At , the displacement of the particle is nearly 
(b) The velocity and acceleration of the particle at t = 0 are a and –ab
respectively
(c) The particle cannot go beyond
(d) The particle will not come back to its starting point at t ? 8
6. The deceleration experienced by a moving motor boat after its engine is
cut off, is given by dv/dt = – kv
3
 where k is a constant. If v
0
 is the
magnitude of the velocity at cut-off, the magnitude of the velocity at a
time t after the cut-off is
(a)
(b) v
0 
e
–kt
(c) v
0 
/ 2
(d) v
0
7. A car, starting from rest, accelerates at the rate f through a distance S,
then continues at constant speed for time t and then decelerates at the
rate  to come to rest. If the total distance traversed is 15 S , then
(a) S = 
(b) S = f t
(c) S = 
(d) S = 
8. A stone falls freely  under gravity. It covers distances h
1
, h
2
 and h
3
 in
the first 5 seconds, the next 5 seconds and the next 5 seconds
respectively. The relation between h
1
, h
2
 and h
3
 is
(a) h
1
 =  = 
(b) h
2
 = 3h
1
 and h
3
 = 3h
2
(c) h
1
 = h
2
 = h
3
(d) h
1
 = 2h
2
 = 3h
3
9. Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0
in the same direction along a straight line. The velocity time graph of
two cars is shown in figure. The time when the car B will catch the car
A, will be
(a) t = 21 sec.
(b) t = 
(c) t =  20 sec.
(d) None of these
10. A body starts from rest and travels a distance x with uniform
acceleration, then it travels a distance 2x with uniform speed, finally it
travels a distance 3x with uniform retardation and comes to rest. If the
complete motion of the particle is along a straight line, then the ratio of
its average velocity to maximum velocity is
(a) 2/5
(b) 3/5
(c) 4/5
(d) 6/7
11. A particle starts its motion from rest under the action of a constant
force. If the distance covered in first 10 seconds is S
1
 and that covered
in the first 20 seconds is S
2
, then:
(a) S
2
 = 3S
1
  (b) S
2
 = 4S
1
 
(c) S
2
 = S
1
  (d) S
2
 = 2S
1
12. A boat takes 2 hours to travel 8 km and back in still water lake. With
water velocity of 4 km h
–1
, the time taken for going upstream of 8 km
and coming back is
(a) 160 minutes
(b) 80 minutes
(c) 100 minutes
(d) 120 minutes
13. A particle moving along x-axis has acceleration f, at time t, given by
, where f
0
 and T are constants. The particle at t = 0 has
zero velocity. In the time interval between t = 0 and the instant when f =
0, the particle’s velocity (v
x
) is
(a) f
0
T
2
(b) f
0
T
2
(c) f
0
T
(d) f
0
T