Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

$ABC$ lies along the line of greatest slope on a plane inclined at angle $\alpha$ to the horizontal, with $\sin\alpha = 0.28$ and $\cos\alpha = 0.96$. Point $A$ is at the top of the plane, point $C$ is at the bottom of the plane, and $AC$ has length $5\,\text{m}$. The section of the plane above the level of $B$ is smooth, while the section below the level of $B$ is rough. A particle $P$ is released from rest at $A$ and reaches $C$ with speed $2\,\text{m s}^{-1}$. The coefficient of friction between $P$ and the part of the plane below $B$ is $0.5$.
(i(a))[3]

Calculate the acceleration of $P$ as it travels from $A$ to $B$.

(i(b))[3]

Calculate the acceleration of $P$ as it moves from $B$ to $C$.

(ii)[3]

Calculate the distance $AB$.

(iii)[3]

Calculate the time taken for $P$ to travel from $A$ to $C$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The acceleration is $2.8\,\text{m s}^{-2}$, from $a = g\sin\alpha$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI