Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A bus runs between stops $A$ and $B$. It leaves $A$ from rest and speeds up at a constant rate of $a\,\text{m s}^{-2}$ until its speed is $16\,\text{m s}^{-1}$. It then continues at this fixed speed before slowing at a constant rate of $0.75\,\text{m s}^{-2}$, finally coming to rest at $B$. The whole journey lasts $240\,\text{s}$.
(a)[1]
Sketch the velocity-time graph for the bus’s trip from $A$ to $B$.
(b)[2]
Find an expression, in terms of $a$, for the amount of time the bus is moving at constant speed.
(c)[3]
Given that the distance from $A$ to $B$ is $3000\,\text{m}$, find the value of $a$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct velocity-time graph shape, beginning at $O$ and ending on the $t$-axis” …