A force F acting on a body depends on its displacement s as ${\mathrm{F\alpha s}}^{-1/3}.$ The power delivered by F will depend on displacement as

Given,

$\mathrm{F} \propto {\mathrm{s}}^{\frac{-1}{3}}$

We know that,

force F = ma

$\mathrm{F}=\mathrm{mv}\frac{\mathrm{dv}}{\mathrm{ds}}$

$\mathrm{mv}\frac{\mathrm{dv}}{\mathrm{ds}}=\mathrm{k}{s}^{\frac{-1}{3}}$

$\mathrm{vdv}=\frac{\mathrm{k}}{\mathrm{m}}{\mathrm{s}}^{\frac{-1}{3}}\mathrm{ds}$

$\int \mathrm{vdv}=\frac{\mathrm{k}}{\mathrm{m}}\int {\mathrm{s}}^{\frac{-1}{3}}\mathrm{ds}$

$\frac{{\mathrm{v}}^2}{2}=\frac{\mathrm{k}}{\mathrm{m}}\times \frac{3}{2}{\mathrm{s}}^{\frac{2}{3}}$

$\mathrm{v}=\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}{\mathrm{s}}^{\frac{-1}{3}}$

$\mathrm{P}=\mathrm{k}\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}{\mathrm{s}}^0$

$\mathrm{P}\propto {\mathrm{s}}^0$

Hence the correct answer is ${\mathrm{s}}^0$.