a
If power is constant

\(P=\text { const. }\)

\(P=F v=\frac{m v^{2} d v}{d x}\)

\(\int_{0}^{x} \frac{P}{m} d x=\int_{0}^{v} v^{2} d v\)

\(\frac{P x}{m}=\frac{v^{3}}{3}\)

\(\left(\frac{3 P x}{m}\right)^{1 / 3}=v=\frac{d x}{d t}\)

\(\left(\frac{3 P}{m}\right)^{1 / 3} \int_{0}^{t} d t=\int_{0}^{x} x^{-1 / 3} d x\)

\(\Rightarrow x=\left(\frac{8 P}{9 m}\right)^{1 / 2} t^{3 / 2}\)