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 tStep1: Given dataA body is initially at rest. It undergoes one-dimensional motion with constant acceleration.Step2: Formula used$P=Fv\left[whereP=power,F=force,v=velocity\right]$Step3: SolutionUsing the first equation of motion$v=u+at\left[wherev=finalvelocity,u=initialvelocity,a=acceleration,t=time\right]$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+at\phantom{\rule{0ex}{0ex}}v=at$We know that the force is the product of mass and acceleration $F=ma$Therefore power becomes,$P=Fv\phantom{\rule{0ex}{0ex}}P=ma×at\phantom{\rule{0ex}{0ex}}P=m{a}^{2}t$Here, mass and acceleration both are constant. Therefore power is directly proportional to time.$P\propto t$Hence, option B is the correct answer.

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