A force F acting on a body depends on its displacement s as $\mathrm{F}\propto {\mathrm{s}}^{\raisebox{1ex}{$-2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$. The power delivered by F will depend on displacement as

$F\propto S^{-2/3}$

$F=k{S}^{-2/3}$

$ma=k{S}^{-2/3}$

$a=\frac{k}{m}{S}^{-2/3}$

Where  $a=v\frac{dv}{ds}$

$v\frac{dv}{ds}=\frac{k}{m}{S}^{-2/3}$

$vdv=\frac{k}{m}{S}^{-2/3}ds$

$\int vdv=\int \frac{k}{m}{S}^{-2/3}ds$

${\mathrm{V}}^2\propto {\mathrm{S}}^{1/3}$

$\mathrm{v}\propto {\mathrm{S}}^{1/6}$

but power $p=FV$

$\mathrm{p}\propto {\mathrm{S}}^{-2/3}\cdot {\mathrm{S}}^{1/6}$

$\mathrm{p}\propto {\mathrm{S}}^{-3/6}$

$\mathrm{p}\propto {\mathrm{S}}^{-1/2}$