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(C) Power $P$ is given by $P = Fv$, where $F$ is force and $v$ is velocity.Since $P$ is constant, $Fv = 	ext{constant}$.Using Newton's second law, $F

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$t^{3/2}$

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(C) Power $P$ is given by $P = Fv$, where $F$ is force and $v$ is velocity.Since $P$ is constant, $Fv = 	ext{constant}$.Using Newton's second law, $F = ma$, so $(ma)v = 	ext{constant}$.Since $a = \frac{dv}{dt}$ and $v = \frac{ds}{dt}$, we have $m \left(\frac{dv}{dt}ight)v = P$.$mv \, dv = P \, dt$.Integrating both sides: $\int mv \, dv = \int P \, dt \implies \frac{1}{2}mv^2 = Pt$.Thus, $v^2 \propto t$, which means $v \propto t^{1/2}$.Since $v = \frac{ds}{dt}$, we have $\frac{ds}{dt} \propto t^{1/2}$.Integrating with respect to time: $s \propto \int t^{1/2} \, dt$.$s \propto t^{3/2}$.

$A$ body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to:

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