The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^{2}-{\mathrm{dt}}^{4}$. The initial velocity and acceleration are, respectively:

 1 $$\mathrm{b}, ~\mathrm{-4d}$$ 2 $$\mathrm{-b},~ \mathrm{2c}$$ 3 $$\mathrm{b}, ~\mathrm{2c}$$ 4 $$\mathrm{2c}, ~\mathrm{-2d}$$
Subtopic:  Non Uniform Acceleration |
81%
From NCERT
PMT - 1999
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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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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. $$10$$ ${\mathrm{ms}}^{-1}$
2. $$18$$ ${\mathrm{ms}}^{-1}$
3. $$14$$ ${\mathrm{ms}}^{-1}$
4. $$26$$ ${\mathrm{ms}}^{-1}$

Subtopic:  Non Uniform Acceleration |
71%
From NCERT
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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $\mathrm{v}\left(\mathrm{x}\right)$ $={\mathrm{\beta x}}^{-2\mathrm{n}}$ where $\mathrm{\beta }$ and $$\mathrm{n}$$ are constants and $$\mathrm{x}$$ is the position of the particle. The acceleration of the particle as a function of $$\mathrm{x}$$ is given by:
1. $-2{\mathrm{n\beta }}^{2}{\mathrm{x}}^{-2\mathrm{n}-1}$
2. $-2{\mathrm{n\beta }}^{2}{\mathrm{x}}^{-4\mathrm{n}-1}$
3. $-2{\mathrm{\beta }}^{2}{\mathrm{x}}^{-2\mathrm{n}+1}$
4. $-2{\mathrm{n\beta }}^{2}{\mathrm{x}}^{-4\mathrm{n}+1}$

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 = – aω2sinωt. The displacement of this particle at a time t will be:

1. $-\frac{1}{2}\left({\mathrm{a\omega }}^{2}\mathrm{sin\omega t}\right){\mathrm{t}}^{2}$

2. $\mathrm{a\omega sin\omega t}$

3. $\mathrm{a\omega cos\omega t}$

4. $\mathrm{asin\omega t}$

Subtopic:  Non Uniform Acceleration |
59%
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 particle is moving along the x-axis such that its velocity varies with time as per the equation $\mathrm{v}=20\left(1-\frac{\mathrm{t}}{2}\right)$. 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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A point moves in a straight line under the retardation a${\mathrm{v}}^{2}$. If the initial velocity is $$\mathrm{u},$$ the distance covered in $$\mathrm{t}$$ seconds is:
1. $\mathrm{aut}$
2. $\frac{1}{\mathrm{a}}\mathrm{ln}$ $\left(\mathrm{aut}\right)$
3. $\frac{1}{\mathrm{a}}\mathrm{ln}$ $\left(1+\mathrm{aut}\right)$
4. $\mathrm{a}$ $\mathrm{ln}$ $\left(\mathrm{aut}\right)$

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. $v=u+at$

4. v = u

Subtopic:  Non Uniform Acceleration |
From NCERT
PMT - 1981
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