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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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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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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If a body is thrown up with the velocity of \(15\) m/s, then the maximum height attained by the body is: (assume \(g = 10\) m/s2
1. \(11.25\) m
2. \(16.2\) m
3. \(24.5\) m
4. \(7.62\) m

Subtopic:  Uniformly Accelerated Motion |
 89%
From NCERT
PMT - 2003
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If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three seconds, the time of the travel is:
1. \(6\) sec
2. \(5\) sec
3. \(4\) sec
4. \(3\) sec

Subtopic:  Uniformly Accelerated Motion |
 67%
From NCERT
PMT - 2004
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A particle moving in a straight line covers half the distance with a speed of \(3~\text{m/s}\). The other half of the distance is covered in two equal time intervals with speeds of \(4.5~\text{m/s}\) and \(7.5~\text{m/s}\) respectively. The average speed of the particle during this motion is:
1. \(4.0~\text{m/s}\)
2. \(5.0~\text{m/s}\)
3. \(5.5~\text{m/s}\)
4. \(4.8~\text{m/s}\)

Subtopic:  Average Speed & Average Velocity |
 70%
From NCERT
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