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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


A

t1/2

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B

t

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C

t3/2

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D

t2

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Solution

The correct option is B

t


Step1: Given data

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration.

Step2: Formula used

P=Fv[whereP=power,F=force,v=velocity]

Step3: Solution

Using the first equation of motion

v=u+at[wherev=finalvelocity,u=initialvelocity,a=acceleration,t=time]

It is given to us that the body is initially at rest which means the initial velocity is zero (the body is not moving at all). u=0

v=0+atv=at

We know that the force is the product of mass and acceleration F=ma

Therefore power becomes,

P=FvP=ma×atP=ma2t

Here, mass and acceleration both are constant. Therefore power is directly proportional to time.

Pt

Hence, option B is the correct answer.


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