Probability — practice question

On a smooth horizontal surface, fixed points $O$ and $A$ are $0.8\,\text{m}$ apart. A particle $P$ with mass $0.25\,\text{kg}$ is projected horizontally from $A$ at $3\,\text{m s}^{-1}$ in the direction away from $O$. When the displacement of $P$ from $O$ is $x\,\text{m}$, its speed is $v\,\text{m s}^{-1}$. The motion of $P$ is resisted by a force of magnitude $k v^2 x^{-2}\,\text{N}$.