\[(a)\;t^{\large\frac{1}{2}} \quad (b)\;t^{\large\frac{3}{2}} \quad (c)\;t^{\large\frac{3}{4}} \quad (d)\;t^2\]

Answer: $t^{\large\frac{3}{2}}$

Power $ P = F\;v = ma\; v$

Acceleration $a = \large\frac{S}{t^2}$ and Velocity $v = \large\frac{S}{t}$, where $S$ is the distance moved.

Since the Power $P$ and mass $m$ are constant, we get

$P = \large\frac{mS}{t^2}$$\times \large\frac{S}{t}$$\rightarrow S^2 = t^3 \rightarrow S \propto t^{\large\frac{3}{2}}$

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