A-level · Kinematics

Constant acceleration (suvat)Exam-style questions

The five suvat equations, why they all fall out of the velocity–time graph (gradient = acceleration, area = displacement), and the one condition that makes them valid — constant acceleration.

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

DifficultyAll Level 2 Level 3 Level 4

1
The points $A$ and $B$ are $480$ m apart on a straight horizontal road.

A coach moves along the road from $A$ to $B$ with constant acceleration. The coach passes $A$ with speed $u\ \text{m s}^{-1}$ and reaches $B$ exactly $24$ s later, when its speed is $25\ \text{m s}^{-1}$

The coach is modelled as a particle.
(a) Show that $u = 15$

(2 marks)
(b) Find the time the coach takes to travel the first half of the distance from $A$ to $B$ .

(5 marks)

The coach has mass $12\,000$ kg. Between $A$ and $B$ , the resistance to the motion of the coach is modelled as a constant force of magnitude $1500$ N.
(c) Use the model to find the constant driving force of the coach's engine between $A$ and $B$ .

(3 marks)
Level 4 · 10 marksTry it
2
[In this question, $\mathbf{i}$ and $\mathbf{j}$ are horizontal unit vectors and position vectors are given relative to a fixed origin $O$ .]

A drone flies at a constant height above horizontal ground. The drone is modelled as a particle $D$ which moves with constant acceleration $(0.5\mathbf{i} + 1.5\mathbf{j})\ \text{m s}^{-2}$

Time $t$ is measured in seconds. When $t = 0$ , $D$ is at the point $A$ and is moving with velocity $(6\mathbf{i} - 9\mathbf{j})\ \text{m s}^{-1}$ . Four seconds later, $D$ is at the point $B$ .
(a) Find the speed of $D$ at $B$ .

(4 marks)

The point $A$ has position vector $(-50\mathbf{i} + 8\mathbf{j})$ m.

When $t = T$ , where $T > 4$ , $D$ is at the point $C$ , which has position vector $(c\mathbf{i} - 7\mathbf{j})$ m.
(b) Find the value of $T$ .

(3 marks)
(c) Find the value of $c$ .

(3 marks)
Level 4 · 10 marksTry it