(i)[2]
Show that the differential equation $v\frac{dv}{dx} = 5 - 0.5v^2$ is obtained.
(ii)[4]
Write $v$ as a function of $x$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle $P$ with mass $0.4\,\text{kg}$ is let go from rest at point $O$ on a smooth plane that is inclined at $30^{\circ}$ to the horizontal. $P$ travels down the line of greatest slope passing through $O$. Its speed is $v\,\text{m}\,\text{s}^{-1}$ when its displacement from $O$ is $x\,\text{m}$. A retarding force of magnitude $0.2v^2\,\text{N}$ acts on $P$ in the direction $PO$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses Newton’s Second Law along the slope: $0.4v\frac{dv}{dx}=0.4g\sin30-0.2v^{2}$ (accept $a$ in place of $v\frac{dv}{dx}$).” …
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