c
(c)\(P = Fv = mav = m\left( {\frac{{dv}}{{dt}}} \right)\;v\) \(⇒\) \(\frac{P}{m}dt = v\;dv\)
\(⇒\)\(\frac{P}{m} \times t = \frac{{{v^2}}}{2}\) \(⇒\) \(v = {\left( {\frac{{2P}}{m}} \right)^{1/2}}{(t)^{1/2}}\)
Now \(s = \int_{}^{} {v\;dt = \int_{}^{} {{{\left( {\frac{{2P}}{m}} \right)}^{1/2}}{t^{1/2}}dt} } \)
 \(s = {\left( {\frac{{2P}}{m}} \right)^{1/2}}\left[ {\frac{{2{t^{3/2}}}}{3}} \right]\) \(⇒\) \(s \propto {t^{3/2}}\)