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Question

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to (i) t⅟² (ii) t (iii) t³́² (iv) t²

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Solution

The body starts from rest so,its initial velocity is zero.

The final velocity of the moving body is given as,

v=u+at

where, v is the final velocityof the body, u is the initial velocityof the body, a is the acceleration with which the body is moving and t is the time taken.

By substitutingthe value of u in the above equation, we get

v=at

The power delivered to the body is given as,

P=Fv

where, F is the force experienced by the body which is calculatedbythe product of mass and acceleration of the body.

By substituting the value of Fand vin the above equation, we get

P=( ma )( at ) =m a 2 t

Since, the body is moving with a constant acceleration therefore,

Pt

Thus, option (ii) is correct.


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