(i)[2]
Show that $3v^{\frac{1}{2}}\,\frac{dv}{dx} = 2$.
(ii)[4]
Express $v$ in terms of $x$.
(iii)[3]
Given that $AB = 7\,\text{m}$, determine the value of $t$ when $P$ passes through $B$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
$O$, $A$ and $B$ are three points lying on one straight line on a smooth horizontal surface. A particle $P$ of mass $0.6\,\text{kg}$ travels along the line. At time $t\,\text{s}$, the particle’s displacement from $O$ is $x\,\text{m}$ and its speed is $v\,\text{m s}^{-1}$. The only horizontal force on $P$ has magnitude $0.4v^{\frac{1}{2}}\,\text{N}$ and acts in the direction $OA$. At the start, the particle is at $A$, where $x = 1$ and $v = 1$.