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

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

$\frac{1}{2} \frac{{mv}^{2}}{T^{2}} t$

$\frac{1}{2} \frac{{mv}^{2}}{T^{2}} t^{}$

answer is A.

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Detailed Solution

We know that,

$P_{i n s t} = F_{i n s t} \times v_{i n s t}$

Force is constant since the acceleration was constant.

$F_{i n s t} = F_{c o n s t} = m a$

$a = \frac{v}{T}$

$v_{i n s t} = (a \times t)$

$v_{i n s t} = \frac{v}{T} \times t$

$P_{i n s t} = (m \times \frac{v}{T}) \times (\frac{v}{T} \times t) \Rightarrow P_{i n s t} = \frac{m v^{2}}{T^{2}} t$

Hence the correct answer is $\frac{m v^{2}}{T^{2}} t .$

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