# A body of mass m  accelerates uniformly from rest   to   in time   The instantaneous power delivered to the body as a function of time t is Option 1) Option 2) Option 3) Option 4)

As we learnt in

Power if the force is constant -

$P=\frac{dw}{dt}= P= \vec{F}\cdot \vec{v}$

- wherein

$\vec{F}\rightarrow force$

$\vec{v}\rightarrow velocity$

Initial velocity = 0

Final velocity = v1

Time taken = t1

Acceleration $=\frac{v_{1}}{t_{1}}$

$\therefore$    velocity at time $t=(\frac{v_{1}}{t_{1}})t$

Power delivered at time t

= F. v

= ma .v

$P=m(\frac{v_{1}}{t_{1}}).(\frac{v_{1}}{t_{1}})t$

$P=m\frac{v_{1}^{2}}{t_{1}^{2}} t$

Option 1)

This is an incorrect option.

Option 2)

This is the correct option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.

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