(i)[3]
Show that, as the particle moves, $v\frac{dv}{dx} = -4 - \frac{2}{x}$.
(ii)[5]
It is given that $P$ is momentarily at rest between $x = 2.0$ and $x = 2.1$. Find the set of possible values of $U$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
$O$ and $A$ are fixed points on a rough horizontal surface, where $OA = 1\,\text{m}$. A particle $P$ of mass $0.4\,\text{kg}$ is projected from $A$ horizontally in the direction $OA$ with speed $U\,\text{m s}^{-1}$ and travels along a straight line. After projection, when $P$ is $x\,\text{m}$ from $O$, its velocity is $v\,\text{m s}^{-1}$. The coefficient of friction between the surface and $P$ is $0.4$. A force of magnitude $\frac{0.8}{x}\,\text{N}$ acts on $P$ in the direction $PO$.