# 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 $v={\left(180-16x\right)}^{1/2}$ 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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