(i)[6]
Set up a differential equation involving $v$ and $x$. By solving it, show that $v = 10 - 2x$.
(ii)[5]
Find $x$ in terms of $t$, and hence prove 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 on a smooth horizontal surface. $P$ begins at $O$ with speed $10\,\text{m s}^{-1}$ and travels towards a fixed point $A$ on the line. At time $t\,\text{s}$, 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 $O$.