How do we describe and calculate motion using speed, velocity, acceleration and motion graphs?
The difference between scalars and vectors, the speed and acceleration equations, average and instantaneous speed, and reading distance-time and velocity-time graphs including gradient and area.
A focused CCEA GCSE Single Award Science answer on motion, covering scalars and vectors, the speed and acceleration equations, average and instantaneous speed, and how to read distance-time and velocity-time graphs including gradient and area.
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What this dot point is asking
CCEA wants you to tell scalars from vectors, use the speed and acceleration equations, distinguish average and instantaneous speed, and read distance-time and velocity-time graphs including the meaning of the gradient and the area.
Scalars and vectors
Distance is how far an object travels, regardless of direction; velocity is speed in a stated direction, so it is a vector.
The speed and acceleration equations
The average speed uses the total distance over the total time; the instantaneous speed is the speed at one moment, such as a speedometer reading. Typical everyday speeds are useful to know: walking is about 1.5 m/s, running about 3 m/s, and cycling about 6 m/s, and the speed of sound in air is about 330 m/s.
Reading motion graphs
Examples in context
- Example 1. Why average and instantaneous speed differ
- On a car journey you might stop at lights, speed up on a clear road and slow in traffic. The instantaneous speed changes all the time, but the average speed is just the whole distance divided by the whole time, including the stops. This is why an average speed of 50 km/h can hide a top speed far higher, a common CCEA distinction.
- Example 2. Reading a journey from a distance-time graph
- A graph that rises steeply, then goes flat, then rises gently tells a story: the object moved fast, then stopped (the flat part), then moved off slowly. Being able to translate the shape of the line into what the object was doing is exactly the skill CCEA tests in motion-graph questions, with the gradient giving the speed at each stage.
- Example 3. Finding distance from a velocity-time graph
- Suppose a cyclist accelerates steadily from rest to 8 m/s over 4 s. On a velocity-time graph this is a straight line from the origin up to 8 m/s. The distance travelled is the area under that line, a triangle of base 4 s and height 8 m/s, which is one half times 4 times 8, or 16 m. Splitting a velocity-time graph into triangles and rectangles to find the area, and so the distance, is a standard CCEA technique, and it works even when the motion has several stages of different acceleration.
Try this
Q1. State the speed of a car that travels 150 m in 10 s. [1 mark]
- Cue. Speed equals 150 divided by 10, which is 15 m/s.
Q2. On a velocity-time graph, what does the area under the line represent? [1 mark]
- Cue. The distance travelled.
Exam-style practice questions
Practice questions written in the style of CCEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
CCEA SAS 20204 marksA car starts from rest and reaches 20 m/s in 8 s. Calculate its acceleration, and then the distance it travels in a further 10 s at this steady speed.Show worked answer →
Four marks for the acceleration and the distance.
Acceleration equals change in velocity divided by time: (20 minus 0) divided by 8, which equals 2.5 m/s squared.
For the steady-speed part, use distance equals speed times time.
Distance equals 20 times 10, which equals 200 m.
So the acceleration is 2.5 m/s squared and the car travels 200 m at steady speed. Markers reward the correct formula, working and units for each part.
CCEA SAS 20193 marksDescribe what the gradient and a horizontal line tell you on a distance-time graph.Show worked answer →
Three marks for the meaning of the gradient and the flat line.
The gradient (steepness) of a distance-time graph equals the speed: a steeper line means a faster speed.
A straight sloping line means a constant (steady) speed.
A horizontal (flat) line means the object is stationary, because the distance is not changing.
Markers reward gradient equals speed, steeper means faster, and flat means stationary.
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Sources & how we know this
- CCEA GCSE Science: Single Award specification — CCEA (2017)