The displacement of the particle varies with time according to the relation x=kb[1ebt]. Then the velocity of the particle is

(1) k(ebt)

(2) kb2ebt

(3) kbebt

(4) None of these 

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 58%
From NCERT
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The acceleration of a particle starting from rest varies with time according to the relation A = – aω2sinωt. The displacement of this particle at a time t will be:

1. 12(2sinωt)t2

2. aωsinωt

3. aωcosωt

4. asinωt

Subtopic:  Non Uniform Acceleration |
 60%
From NCERT
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If the velocity of a particle is (10 + 2t2) m/s, then the average acceleration of the particle between 2 sec and 5 sec is:

(1) 2 m/s2

(2) 4 m/s2

(3) 12 m/s2

(4) 14 m/s2

Subtopic:  Acceleration |
 54%
From NCERT
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A thief is running away on a straight road in a jeep moving with a speed of 9 ms–1. A policeman chases him on a motor cycle moving at a speed of 10 ms–1. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the policeman to catch the thief?

1. 1 s 2. 19 s
3. 90 s 4. 100 s
Subtopic:  Relative Motion in One Dimension |
 83%
From NCERT
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A car A is travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which is moving with a speed of 70 km/h. When the distance between them is 2.5 km, the car B is given a deceleration of 20 km/h2. After how much time will B catch up with A

(1) 1 hr

(2) 1/2 hr

(3) 1/4 hr

(4) 1/8 hr

Subtopic:  Acceleration |
 66%
From NCERT
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The speed of a body moving with uniform acceleration is u. This speed is doubled while covering a distance S. When it covers an additional distance S, its speed would become

(1) 3u

(2) 5u

(3) 11u

(4) 7u

Subtopic:  Uniformly Accelerated Motion |
 56%
From NCERT
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Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are 0.3 m/s2 and 0.2 m/s2 respectively, then the time they take to pass each other will be

1.  5 s
2.  10 s
3.  15 s
4.  20 s

Subtopic:  Relative Motion in One Dimension |
 68%
From NCERT
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A body starts from rest with uniform acceleration. If its velocity after n second is v, then its displacement in the last two seconds is

(1) 2v(n+1)n

(2) v(n+1)n

(3) v(n-1)n

(4) 2v(n-1)n

Subtopic:  Acceleration |
 65%
From NCERT
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A particle is moving in a straight line and passes through a point O with a velocity of 6 ms–1. The particle moves with a constant retardation of 2 ms–2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

(1) 3s

(2) 8s

(3) Never

(4) 4s

Subtopic:  Acceleration |
 57%
From NCERT
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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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