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Complete Question Bank + Test Series
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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.

3.

4.

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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 $\left(4{t}^{3}-2t\right)$, 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/s2

(2) 22 m/s2

(3) 12 m/s2

(4) 10 m/s2

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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

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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/sec2. 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/s2 . After 8s, a stone is released from the balloon. The stone will (g = 10 m/s2

(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 v0 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) ${v}_{0}t+\frac{1}{2}b{t}^{2}$

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The acceleration of a particle starting from rest, varies with time according to the relation A = – 2 sinω 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) $a\text{\hspace{0.17em}}\mathrm{sin}\omega \text{\hspace{0.17em}}t$