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A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time 't' is proportional to

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$t^{1/2}$

$t^{3/4}$

$t^{3/2}$

$t^{2}$

answer is C.

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Detailed Solution

$P = F \times V$

$= ma \times at$

$= {ma}^{2} t$

This means $a^{2} t = \frac{P}{m} = constant$

Distance $s = \frac{1}{2} {at}^{2}$

$s^{2} = \frac{1}{4} a^{2} t^{4} = {constant.t}^{3}$

Thus we have $s \propto t^{3/2}$

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