(i)[2]
Show that $v\frac{dv}{dx} = kx$ and state the value of $k$.
(ii)[3]
Find the value of $x$ at the instant when $P$ comes to instantaneous rest.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle $P$ with mass $0.3\,\text{kg}$ travels along a straight line on a smooth horizontal surface. $P$ passes through a fixed point $O$ on the line with velocity $8\,\text{m s}^{-1}$. A force of magnitude $2x\,\text{N}$ acts on $P$ in the direction $PO$, where $x\,\text{m}$ is the displacement of $P$ from $O$.