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

Kinematics of motion in a straight line — practice question

A ball travels along the horizontal surface of a billiards table, slowing down with constant deceleration of magnitude $d\,\text{m s}^{-2}$. It leaves $A$ at speed $1.4\,\text{m s}^{-1}$ and, $1.2\,\text{s}$ later, arrives at the table edge at $B$ with speed $1.1\,\text{m s}^{-1}$.
(i)[3]

Find the distance $AB$ and determine the value of $d$.

(ii)[3]

$AB$ meets the edge of the table containing $B$ at right angles. A low wall runs along every edge of the table, and the ball bounces off the wall at $B$ before moving straight towards $A$. The ball finally stops at $C$, where $BC$ is $2\,\text{m}$. Find the speed with which the ball begins to move towards $A$ and the time taken for the ball to go from $B$ to $C$.

(iii)[2]

Sketch the velocity-time graph for the ball's motion, from the moment it leaves $A$ until it stops at $C$, and show on the axes the velocity and time values when the ball is at $A$, at $B$ and at $C$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $s = \tfrac12(u+v)t$ or $v = u + at$ to determine the distance” …

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