Probability — practice question

A particle $P$ with mass $0.4\,\text{kg}$ is launched horizontally from point $O$ across a smooth horizontal plane. After $t\,\text{s}$ have elapsed since projection, the velocity of $P$ is $v\,\text{m s}^{-1}$. A force of magnitude $0.8t\,\text{N}$ acting away from $O$ is applied to $P$, while a force of magnitude $2e^{-t}\,\text{N}$ acts opposite to the motion of $P$.