Probability — practice question

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