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

Kinematics of motion in a straight line — practice question

$A$, $B$ and $C$ are three points on the line of greatest slope of a smooth plane that is inclined at an angle of $\theta^\circ$ to the horizontal. Point $A$ lies above $B$ and $B$ lies above $C$, while the distances $AB$ and $BC$ are $1.76\,\text{m}$ and $2.16\,\text{m}$ respectively. A particle slides down the plane with constant acceleration $a\,\text{m s}^{-2}$. The particle’s speed at $A$ is $u\,\text{m s}^{-1}$. It takes $0.8\,\text{s}$ for the particle to move from $A$ to $B$ and $1.4\,\text{s}$ to move from $A$ to $C$.
(i)[6]

Find the values of $u$ and $a$ from the information provided.

(ii)[2]

Find the value of $\theta$ in degrees.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Applies $s = ut + \tfrac{1}{2}at^2$ to $AB$, so $1.76 = 0.8u + 0.32a$

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