A-level · Kinematics

Motion graphs (displacement–time & velocity–time)Exam-style questions

What the gradient and the area mean on each kind of motion graph — gradient of displacement–time is velocity, gradient of velocity–time is acceleration, area under velocity–time is displacement — and how to model a journey as a graph and read unknowns off its area.

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
A straight horizontal road passes through the points $A$ $A$ and $B$ $B$ .Figure 1 (not accurately drawn)

A van $P$ $P$ leaves $A$ $A$ from rest at time $t = 0$ $t = 0$ and travels along the road towards $B$ $B$ , where $t$ $t$ is measured in seconds. Figure 1 shows the speed-time graph for the motion of the van for $0 \leqslant t \leqslant 25$ $0 ⩽ t ⩽ 25$
- The van accelerates uniformly from rest for $8$ seconds, reaching a speed of $V\ \text{m s}^{-1}$
- The van then moves at the constant speed $V\ \text{m s}^{-1}$
- The van passes $B$ when $t = 25$
The distance from $A$ $A$ to $B$ $B$ is $336$ $336$ m.
(a) Show that $V = 16$ $V = 16$

(3 marks)
(b) Find the acceleration of the van during the first $8$ $8$ seconds of its motion.

(2 marks)

After passing $B$ $B$ , the van continues along the road at the constant speed $V\ \text{m s}^{-1}$ $V m s^{- 1}$

A car $Q$ $Q$ leaves $A$ $A$ from rest when $t = 5$ $t = 5$ and travels along the road in the same direction as the van. The car accelerates uniformly for $T$ $T$ seconds until its speed is $20\ \text{m s}^{-1}$ $20 m s^{- 1}$ , and then moves at this constant speed. The car draws level with the van when $t = 45$ $t = 45$

The van and the car are modelled as particles.
(c) On a copy of Figure 1, sketch speed-time graphs for the motion of the van and the motion of the car for $0 \leqslant t \leqslant 45$ $0 ⩽ t ⩽ 45$

(3 marks)
(d) Find the value of $T$ $T$

(5 marks)
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