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

Kinematics of motion in a straight line — practice question

At time $t = 0$, with $t$ measured in seconds, a runner leaves point $P$. The runner is initially at rest, then accelerates at $1.2\,\text{m s}^{-2}$ for $5\,\text{s}$. During the following $12\,\text{s}$ the runner continues at a constant speed, and then decelerates uniformly over $3\,\text{s}$ until coming to rest at $Q$. A cyclist leaves $P$ at time $t = 10$ and accelerates uniformly for $10\,\text{s}$, after which the cyclist immediately decelerates uniformly to rest at $Q$ at time $t = 30$.
(i)[4]

Sketch the runner's velocity-time graph and demonstrate that the distance $PQ$ is $96\,\text{m}$.

(ii)[3]

Determine the magnitude of the cyclist's acceleration.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Three straight lines drawn correctly on the $v$-$t$ graph

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