A body starts from rest and acquires a velocity V in time T. The instantaneous power delivered to the body in time t is proportional to:

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

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

$\frac{V}{T} t$

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

answer is C.

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Detailed Solution

$a = \frac{V - 0}{T} = \frac{V}{T}$

$v = u + a t = 0 + (\frac{V}{T}) t$

$W = \frac{1}{2} {mv}^{2} - 0 = \frac{1}{2} m {(\frac{V}{T} t)}^{2} \frac{W}{t} = \frac{1}{2} m (\frac{V^{2}}{T^{2}}) t P = \frac{1}{2} m \frac{V^{2}}{T^{2}} t$

Power is directly proportional to $\frac{V^{2} t}{T^{2^{}}}$

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