A particle moves along a straight line such that its displacement at any time \(t\) is given by \(S = t^{3} - 6 t^{2} + 3 t + 4\) metres. The velocity when the acceleration is zero is:

1. \(4\) ms-1 2. \(-12\) ms−1
3. \(42\) ms−1 4. \(-9\) ms−1

Subtopic:  Acceleration |
 81%
From NCERT
PMT - 1994
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The position \(x\) of a particle varies with time \(t\) as \(x=at^2-bt^3\). The acceleration of the particle will be zero at time \(t\) equal to:

1. \(\dfrac{a}{b}\) 2. \(\dfrac{2a}{3b}\)
3. \(\dfrac{a}{3b}\) 4. zero
 
Subtopic:  Acceleration |
 85%
From NCERT
PMT - 1997
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The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is: 

1. \(24\) metres 2. \(12\) metres
3. \(5\) metres 4. zero
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
 76%
From NCERT
PMT - 2000
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A student is standing at a distance of \(50\) metres from the bus. As soon as the bus begins its motion with an acceleration of \(1\) ms–2, the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is:
1. \(5\) ms–1
2. \(8\) ms–1
3. \(10\) ms–1
4. \(12\) ms–1

Subtopic:  Uniformly Accelerated Motion |
 73%
From NCERT
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If the velocity of a particle is given by v=(18016x)1/2 m/s, then its acceleration will be: 
1. zero
2. \(8\) m/s2
3. \(-8\) m/s2
4. \(4\) m/s

Subtopic:  Acceleration |
 68%
From NCERT
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Two trains, each \(50\) m long, are travelling in the opposite direction with velocities \(10\) m/s and \(15\) m/s. The time of crossing is:
1. \(10\) sec
2. \(4\) sec
3. \(2\sqrt{3}\) sec
4. \(4\sqrt{3}\) sec

Subtopic:  Relative Motion in One Dimension |
 78%
From NCERT
PMT - 1999
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The distance between two particles is decreasing at the rate of \(6\) m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of \(4\) m/sec. It can be concluded that particles' speeds could be:
1. \(5\) m/sec, \(1\) m/sec
2. \(4\) m/sec, \(1\) m/sec
3. \(4\) m/sec, \(2\) m/sec
4. \(5\) m/sec, \(2\) m/sec

Subtopic:  Relative Motion in One Dimension |
 75%
From NCERT
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A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during which the body rises is: 

1. Equal to the time of fall.
2. Less than the time of fall.
3. Greater than the time of fall.
4. Twice the time of fall.
Subtopic:  Non Uniform Acceleration |
 54%
From NCERT
PMT - 2001
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A body starts to fall freely under gravity. The distances covered by it in the first, second and third second will be in the ratio: 
1. \(1:3:5\)
2. \(1:2:3\)
3. \(1:4:9\)
4. \(1:5:6\)

Subtopic:  Uniformly Accelerated Motion |
 87%
From NCERT
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A body is thrown vertically up from the ground. It reaches a maximum height of \(100\) m in \(5\) s. After what time will it reach the ground from the position of maximum height?
1. \(1.2\) s
2. \(5\) s
3. \(10\) s
4. \(25\) s

Subtopic:  Uniformly Accelerated Motion |
 80%
From NCERT
PMT - 2000
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