What is distance travelled?

The total length of the path; a scalar.

What is acceleration?

The rate of change of velocity.

Which are vectors: speed, velocity, distance, displacement, acceleration?

Velocity, displacement and acceleration.

What does a negative gradient on a displacement-time graph mean?

The velocity is negative: moving in the negative direction.

Why can average velocity be zero while average speed is not?

For a round trip the displacement is zero but the distance travelled is not.

Area of a trapezium for a velocity-time graph?

\frac12(a+b)h where a and b are the parallel sides.

The language of kinematics and motion graphsAQA A-Level Maths: Flashcards

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What is displacement?

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What is displacement?: The change in position; a vector with magnitude and direction.
What is distance travelled?: The total length of the path; a scalar.
Average velocity formula?: $\frac{\text{displacement}}{\text{time}}$ .
Average speed formula?: $\frac{\text{total distance}}{\text{time}}$ .
What is acceleration?: The rate of change of velocity.
Which are vectors: speed, velocity, distance, displacement, acceleration?: Velocity, displacement and acceleration.
Gradient of a displacement-time graph?: The velocity.
Gradient of a velocity-time graph?: The acceleration.
Area under a velocity-time graph?: The displacement.
What does a horizontal line on a displacement-time graph mean?: The object is at rest.
What does a negative gradient on a displacement-time graph mean?: The velocity is negative: moving in the negative direction.
Why can average velocity be zero while average speed is not?: For a round trip the displacement is zero but the distance travelled is not.
Area of a trapezium for a velocity-time graph?: $\frac12(a+b)h$ where $a$ and $b$ are the parallel sides.

Exam questions on The language of kinematics and motion graphs

A runner starts at point $O$ on a straight track and runs $40$ m in the positive direction in $8$ s. She then immediately turns round and runs $15$ m back towards $O$ in $5$ s.
Find the average speed of the runner over the whole $13$ s, and explain why it is different from the magnitude of her average velocity.2 marks
A train travels along a straight track. Its velocity-time graph is made of three straight-line sections: the velocity increases uniformly from $0$ to $20$ m s $^{-1}$ in $10$ s, then stays constant at $20$ m s $^{-1}$ for $30$ s, then decreases uniformly to $0$ in $20$ s.
Find the acceleration of the train in the last $20$ s, and state what the sign of your answer tells you.2 marks
A cyclist travels along a straight road. Her displacement $s$ metres from a point $O$ , at time $t$ seconds, has a displacement-time graph made of three straight-line sections: $s$ increases uniformly from $0$ to $100$ when $t$ goes from $0$ to $20$ ; $s$ stays at $100$ from $t=20$ to $t=50$ ; and $s$ decreases uniformly from $100$ to $40$ from $t=50$ to $t=80$ .
Find the velocity of the cyclist in each of the three stages of her journey.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).