(i)[2]
Show that the relation $2v\frac{dv}{dx} = 10 - (\sqrt{3})x^2$ is obtained.
(ii)[5]
Calculate the maximum speed of $P$.
(iii)[2]
Determine the value of $x$ when $P$ is at rest.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ with mass $0.2\text{ kg}$ is set free from rest at point $O$ on a plane that is inclined at $30^\circ$ to the horizontal. After $t\text{ s}$ from release, $P$ has velocity $v\text{ m s}^{-1}$ and has moved a distance $x\text{ m}$ down the plane from $O$. The coefficient of friction between $P$ and the plane grows as $P$ moves down the plane, and is given by $0.1x^2$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Since $v\,dv/dx = a$ in the direction parallel to the slope, the equation is $0.2v\,dv/dx = 0.2g\sin30 - 0.1x^2(0.2g\cos30)$” …
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