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(C) Power is defined as the rate of doing work, given by $P = Fv$.Since $F = ma = m(dv/dt)$, we have $P = mv(dv/dt) = 	ext{constant} (k)$.Rearranging

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$t^{3/2}$

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(C) Power is defined as the rate of doing work, given by $P = Fv$.Since $F = ma = m(dv/dt)$, we have $P = mv(dv/dt) = 	ext{constant} (k)$.Rearranging the terms, we get $v dv = (k/m) dt$.Integrating both sides, we obtain $v^2/2 = (k/m)t$, which implies $v = \sqrt{2k/m} \cdot t^{1/2}$.Since velocity $v = dx/dt$, we have $dx/dt = \sqrt{2k/m} \cdot t^{1/2}$.Integrating with respect to time $t$, we get $x = \int \sqrt{2k/m} \cdot t^{1/2} dt = \sqrt{2k/m} \cdot (t^{3/2} / (3/2)) = (2/3) \sqrt{2k/m} \cdot t^{3/2}$.Thus, the displacement $x$ is proportional to $t^{3/2}$.

$A$ body is moving unidirectionally under the influence of a source of constant power. Its displacement in time $t$ is proportional to

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