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A point moves in a straight line under the retardation av2. If the initial velocity is u, the distance covered in 't' seconds is-

1.  aut

2.  1aln aut

3.  1aln 1+aut

4.  a ln aut

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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 (4t32t), 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+at2

(2) v=u+at22

(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+0.1t2. 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) v0t+13bt2

(2) v0t+13bt3

(3) v0t+16bt3

(4) v0t+12bt2

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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) 12(aω2sinωt)t2

(2) aωsinωt

(3) aωcosωt

(4) asinωt  

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