(i)[2]
Show that the equation can be written as $3v^{\frac{1}{2}}\frac{dv}{dx} = 2$.
(ii)[4]
Express $v$ as a function of $x$.
(iii)[3]
Given that $AB = 7\,\text{m}$, find the value of $t$ when $P$ passes through $B$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
Points $O$, $A$ and $B$ lie on one straight line on a smooth horizontal plane. A particle $P$ with mass $0.6\,\text{kg}$ travels along the line. At time $t\,\text{s}$, its displacement from $O$ is $x\,\text{m}$ and its speed is $v\,\text{m s}^{-1}$. The only horizontal force acting on $P$ has magnitude $0.4v^{\frac{1}{2}}\,\text{N}$ and is directed along $OA$. At the beginning, the particle is at $A$, so $x = 1$ and $v = 1$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s 2nd law together with $a = v\frac{dv}{dx}$ to produce $0.6v\frac{dv}{dx} = 0.4v^{\frac{1}{2}}$” …
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