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A point moves in a straight line under the retardation a${\mathrm{v}}^{2}$. If the initial velocity is u, the distance covered in '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. $\mathrm{a}\mathrm{ln}\left(\mathrm{aut}\right)$

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A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $(4{t}^{3}-2t)$, where *t* is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 *m* from the origin ?

(1) 28 m/s^{2}

(2) 22 m/s^{2}

(3) 12 m/s^{2}

(4) 10 m/s^{2}

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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*

PMT - 1981

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The velocity of a body depends on time according to the equation $v=20+0.1{t}^{2}$. The body is undergoing

(1) Uniform acceleration

(2) Uniform retardation

(3) Non-uniform acceleration

(4) Zero acceleration

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A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 *m/sec*^{2}. If after 5 *sec* its engine is switched off, the maximum height of the rocket from earth's surface would be ** [MP PET 1995]**

(1) 245 *m*

(2) 490 *m*

(3) 980 *m*

(4) 735 *m*

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A balloon starts rising from the ground with an acceleration of 1.25 *m*/*s*^{2} . After 8s, a stone is released from the balloon. The stone will (*g* = 10 *m*/*s*^{2})

(1) Reach the ground in 4 second

(2) Begin to move down after being released

(3) Have a displacement of 50 *m*

(4) Cover a distance of 40 *m* in reaching the ground

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The acceleration of a particle is increasing linearly with time *t* as *bt*. The particle starts from the origin with an initial velocity *v*_{0} The distance travelled by the particle in time *t* will be

(1) ${v}_{0}t+\frac{1}{3}b{t}^{2}$

(2) ${v}_{0}t+\frac{1}{3}b{t}^{3}$

(3) ${v}_{0}t+\frac{1}{6}b{t}^{3}$

(4) ${v}_{0}t+\frac{1}{2}b{t}^{2}$

PMT - 1995

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The acceleration of a particle starting from rest, varies with time according to the relation *A* = – *aω*^{2} sin*ω t*. The displacement of this particle at a time *t* will be

(1) $-\frac{1}{2}\text{\hspace{0.17em}}\left(a{\omega}^{2}\mathrm{sin}\omega \text{\hspace{0.17em}}t\right)\text{\hspace{0.17em}}{t}^{2}$

(2) $a\omega \text{\hspace{0.17em}}\mathrm{sin}\omega \text{\hspace{0.17em}}t$

(3) $a\omega \text{\hspace{0.17em}}\mathrm{cos}\omega \text{\hspace{0.17em}}t$

(4) **$a\text{\hspace{0.17em}}\mathrm{sin}\omega \text{\hspace{0.17em}}t$ **

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