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(A) The body starts from rest,so initial velocity $u = 0$. Since it is accelerated uniformly to speed $v$ in time $T$,the acceleration $a$ is given by

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$\frac{mv^2}{T^2}t$

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(A) The body starts from rest,so initial velocity $u = 0$. Since it is accelerated uniformly to speed $v$ in time $T$,the acceleration $a$ is given by $a = \frac{v - u}{T} = \frac{v}{T}$. The velocity at any time $t$ is $v(t) = at = \frac{v}{T}t$. The force acting on the body is $F = ma = m\left(\frac{v}{T}\right)$. Instantaneous power $P$ is given by $P = F \cdot v(t)$. Substituting the values,$P = \left(m \frac{v}{T}\right) \left(\frac{v}{T}t\right) = \frac{mv^2}{T^2}t$.

$A$ body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by

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