Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

$A$, $B$ and $C$ are three points along the line of greatest slope on a plane inclined at $\theta^\circ$ to the horizontal, with $A$ above $B$ and $B$ above $C$. The section between $A$ and $B$ is smooth, while the section between $B$ and $C$ is rough. A particle $P$ is released from rest at $A$ and slides down the line $ABC$. $0.8\,\text{s}$ after leaving $A$, the particle passes through $B$ with speed $4\,\text{m s}^{-1}$.
(i)[3]

Calculate the value of $\theta$.

(ii)[5]

At $4.8\,\text{s}$ after leaving $A$, the particle is at rest at $C$. Calculate the coefficient of friction between $P$ and the rough section of the plane.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: For $t<0.8$, the acceleration equals $\frac{4}{0.8}$

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