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

Kinematics of motion in a straight line — practice question

The diagram gives the velocity-time graph for a bus’s motion. The bus begins from rest and accelerates uniformly for $8$ seconds until it reaches $12.6\text{ m s}^{-1}$. It then continues at this speed for $40$ seconds. After that, it slows down uniformly in two stages. From $48$ to $62$ seconds the bus decelerates at $a\text{ m s}^{-2}$, and from $62$ to $70$ seconds it decelerates at $2a\text{ m s}^{-2}$ until it stops.
(a)[1]

Determine the distance travelled by the bus in the first $8$ seconds.

(b)[3]

Determine the value of $a$.

(c)[4]

Find the average speed of the bus over the whole journey.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct distance $50.4\,\text{m}$ (allow $\frac{252}{5}$).

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