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:

\frac{{m v}^{2}}{T^{2}} . t

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\frac{{m v}^{2}}{T^{2}} . t^{2}

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\frac{1}{2} \frac{{m v}^{2}}{T^{2}} . t

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\frac{1}{2} \frac{{m v}^{2}}{T^{2}} . t^{2}

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Solution

The correct option is A $\frac{{m v}^{2}}{T^{2}} . t$
$P_{i n s t} = F_{i n s t} \times v_{i n s t} a s i t w a s g i v e n c o n s t a n t a c c e l e r a t i o n, f o r c e i s a l s o c o n s t a n t . F_{i n s t} = F_{c o n s t} = m a a = \frac{v}{T} . v_{i n s t} = (a \times t) = \frac{v}{T} \times t P_{i n s t} = (m \times \frac{v}{T}) \times (\frac{v}{T} \times t) P_{i n s t} = m \frac{v^{2}}{T^{2}} t$

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