(i)[6]
Set up a differential equation involving $v$ and $x$. Then solve it to show that $v = 10 - 2x$.
(ii)[5]
Express $x$ in terms of $t$, and hence show that the particle is always less than $5\text{ m}$ from $O$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ with mass $0.25\text{ kg}$ travels in a straight line along a smooth horizontal surface. It begins at the point $O$ with speed $10\text{ m s}^{-1}$ and travels towards a fixed point $A$ on the line. After $t\text{ s}$, the displacement of $P$ from $O$ is $x\text{ m}$ and its velocity is $v\text{ m s}^{-1}$. A resistive force of magnitude $(5 - x)\text{ N}$ acts on $P$ in the direction towards $O$.