A particle is projected with velocity v0 along x-axis. The deceleration of the particle is proportional to the square of the distance from the origin i.e., a=αx2. The distance at which the particle stops is :

1.  3v02α
2.  3vo2α13
3.  3v022α
4.  3v022α13  

Subtopic:  Non Uniform Acceleration |
 60%
From NCERT
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A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are

(1) v/2 and v/2

(2) 0 and v/2

(3) 0 and 0

(4) v/2 and 0

Subtopic:  Average Speed & Average Velocity |
 86%
From NCERT
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A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4h. The two stones cross each other after time:

1. h8g

2. 8g h

3. 2g h

4. h2g

Subtopic:  Relative Motion in One Dimension |
 50%
From NCERT
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Four marbles are dropped from the top of a tower one after the other at a one-second interval. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third, and the third and fourth will be, respectively:

1. 35 m, 25 m, and 15 m 2. 30 m, 20 m, and 10 m
3. 20 m, 10 m, and 5 m 4. 40 m, 30 m, and 20 m
Subtopic:  Uniformly Accelerated Motion |
 73%
From NCERT
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A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

(1) 4hg

(2) 2hg

(3) 2hg

(4) gh 

Subtopic:  Uniformly Accelerated Motion |
From NCERT
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Two bodies are thrown simultaneously from a tower with same initial velocity v0 : one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is

(1) 2v0t+12gt2

(2) 2v0t

(3) v0t+12gt2

(4) v0t

Subtopic:  Relative Motion in One Dimension |
 62%
From NCERT
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A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is:

(1) 50 m

(2) 75 m

(3) 100 m

(4) 125 m

Subtopic:  Uniformly Accelerated Motion |
 63%
From NCERT
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A particle is projected upwards. The times corresponding to height h while ascending and while descending are t1 and t2 respectively. The velocity of projection will be:

1. gt1

2. gt2

3. g (t1+t2)

4. g(t1+t2)2

Subtopic:  Uniformly Accelerated Motion |
 69%
From NCERT
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A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u.

(1) They meet at time t=ug and at a height u22g+gT28

(2) They meet at time t=ug+T2 and at a height u22g+gT28

(3) They meet at time t=ug+T2 and at a height u22ggT28

(4) They never meet

Subtopic:  Uniformly Accelerated Motion | Relative Motion in One Dimension |
From NCERT
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Two cars are moving in the same direction with the same speed 30 km/hr. They are separated by a distance of 5 km. The speed of a car moving in the opposite direction, if it meets these two cars at an interval of 4 minutes, will be

1. 40 km/hr

2. 45 km/hr

3. 30 km/hr

4. 15 km/hr

Subtopic:  Relative Motion in One Dimension |
 73%
From NCERT
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