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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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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The motion of a particle along a straight line is described by the equation
$$x=8+12 t-t^3$$ where $$x$$ is in metre and $$t$$ is in second. The retardation of the particle when its velocity becomes zero is:

 1 $$24 ~\text{ms}^{-2}$$ 2 zero 3 $$6 ~\text{ms}^{-2}$$ 4 $$12 ~\text{ms}^{-2}$$
Subtopic:  Non Uniform Acceleration |
73%
From NCERT
NEET - 2012
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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $$v(x)= βx^{- 2 n}$$ where $$\beta$$ and $$n$$ are constants and $$x$$ is the position of the particle. The acceleration of the particle as a function of $$x$$ is given by:
1. $$- 2 nβ^{2} x^{- 2 n - 1}$$
2. $$- 2 nβ^{2} x^{- 4 n - 1}$$
3. $$- 2 \beta^{2} x^{- 2 n + 1}$$
4. $$- 2 nβ^{2} x^{- 4 n + 1}$$
${}^{}$

Subtopic:  Non Uniform Acceleration |
68%
From NCERT
NEET - 2015
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The acceleration of a particle starting from rest varies with time according to the relation $$A= - a\omega^2\sin \omega t$$. The displacement of this particle at a time $$t$$ will be:
1. $$-\frac{1}{2}\left(a\omega^2\sin\omega t\right)t^2$$
2. $$a\omega \sin \omega t$$
3. $$a\omega \cos \omega t$$
4. $$a\sin \omega t$$​​​​​​​

Subtopic:  Non Uniform Acceleration |
59%
From NCERT
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A particle is moving along the $$x$$-axis such that its velocity varies with time as per the equation $$v = 20\left(1-\frac{t}{2}\right)$$. At $$t=0$$ particle is at the origin. From the following, select the correct position $$(x)$$ - time $$(t)$$ plot for the particle:

 1 2 3 4
Subtopic:  Non Uniform Acceleration |
57%
From NCERT
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For the given acceleration $$\left ( a \right )$$ versus time $$\left ( t \right )$$ graph of a body, the body is initially at rest.

From the following, the velocity $$\left ( v \right )$$ versus time $$\left ( t \right )$$ graph will be:

 1 2 3 4

Subtopic:  Non Uniform Acceleration |
61%
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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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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The initial velocity of a particle is $$u$$ (at $$t=0$$) and the acceleration $$f$$ is given by $$at$$. Which of the following relation is valid?
1. $$v = u + a t^{2}$$
2. $$v = u + a \frac{t^{2}}{2}$$
3. $$v = u + a t$$
4. $$v= u$$

Subtopic:  Non Uniform Acceleration |
From NCERT
PMT - 1981
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