# The acceleration $$a$$ (in ${\mathrm{ms}}^{-2}$) of a body, starting from rest varies with time $$t$$ (in $$\mathrm{s}$$) as per the equation $$a=3t+4.$$ The velocity of the body at time $$t=2$$ $$\mathrm{s}$$ will be: 1. $$10~\text{ms}^{-1}$$ 2. $$18~\text{ms}^{-1}$$ 3. $$14~\text{ms}^{-1}$$ 4. $$26~\text{ms}^{-1}$$

Subtopic:  Non Uniform Acceleration |
71%
From NCERT
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A point moves in a straight line under the retardation $$av^2$$${}^{}$. If the initial velocity is $$u,$$ the distance covered in $$t$$ seconds is:
1. $$(aut)$$
2. $$\frac{1}{a}\mathrm{ln}(aut)$$
3. $$\frac{1}{a}\mathrm{ln}(1+aut)$$
4. $$a~\mathrm{ln}(aut)$$

Subtopic:  Non Uniform Acceleration |
56%
From NCERT
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The relation between time and distance is given by $t=\alpha {x}^{2}+\beta x$, where α and β are constants. The retardation, as calculated based on this equation, will be (assume v to be velocity):
1. $2\alpha {v}^{3}$
2. $2\beta {v}^{3}$
3. $2\alpha \beta {v}^{3}$
4. $2{\beta }^{2}{v}^{3}$

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
52%
From NCERT
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The displacement of a particle is given by $$y = a + bt + ct^{2} - dt^{4}$$. The initial velocity and acceleration are, respectively:

 1 $$b, -4d$$ 2 $$-b,2c$$ 3 $$b, ~2c$$ 4 $$2c, -2d$$
Subtopic:  Non Uniform Acceleration |
81%
From NCERT
PMT - 1999
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An elevator car, whose floor to ceiling distance is equal to $$2.7~\text{m}$$, starts ascending with constant acceleration of $$1.2~\text{ms}^{-2}$$. $$2$$ sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is:
1. $$\sqrt{0.54}~\text{s}$$
2. $$\sqrt{6}~\text{s}$$
3. $$0.7~\text{s}$$
4. $$1~\text{s}$$

Subtopic:  Relative Motion in One Dimension |
From NCERT
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The acceleration $$a$$ in m/s2 of a particle is given by $a=3{t}^{2}+2t+2$ where t is the time. If the particle starts out with a velocity, $$u=2$$ m/s at t = 0, then the velocity at the end of $$2$$ seconds will be:
1. $$12$$ m/s
2. $$18$$ m/s
3. $$27$$ m/s
4. $$36$$ m/s

Subtopic:  Acceleration |
73%
From NCERT
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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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