Velocity–Time Graphs
Get to grips with Velocity–Time Graphs for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. On a velocity–time graph the gradient gives the acceleration and the area under the line gives the distance travelled.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
A velocity-time graph shows how velocity varies with time. Two features carry meaning: the gradient gives the acceleration, and the area under the graph gives the distance travelled.
A horizontal line means constant velocity, so the acceleration is zero. A sloping line means constant acceleration, and the steeper the line the greater the acceleration. A line sloping downwards means deceleration.
The distance travelled is found from the area under the line. For a horizontal section this is a rectangle; for a sloping section it is a triangle or trapezium. Splitting the graph into simple shapes and adding their areas is the reliable method.
Revision notes
Gradient gives acceleration
The gradient of a velocity-time graph gives the acceleration.
A horizontal line means zero acceleration and constant velocity. A steeper slope means a greater acceleration. A downward slope means deceleration.
Area gives distance
The area under a velocity-time graph gives the distance travelled.
Split the area into rectangles, triangles and trapeziums, calculate each, and add them. For a curve, count squares or use trapezium strips to estimate.
Comparing with distance-time graphs
On a distance-time graph the gradient is speed and the area means nothing.
On a velocity-time graph the gradient is acceleration and the area is distance. Confusing the two graph types is the most common error in this topic.
Key points
- The gradient gives the acceleration.
- The area under the graph gives the distance travelled.
- A horizontal line means constant velocity.
- A sloping line means constant acceleration.
- A downward slope means deceleration.
- Split the area into simple shapes.
Worked examples
Example 1
An object travels at a constant 12 m/s for 5 seconds. Calculate the distance travelled from the velocity-time graph. [2 marks]
Model answer
The area under the graph is a rectangle: 12 × 5 (1 mark) = 60 m (1 mark).
Example 2
An object accelerates uniformly from rest to 10 m/s in 4 seconds. Calculate the distance travelled. [3 marks]
Model answer
The area under the graph is a triangle (1 mark). Area = ½ × base × height = ½ × 4 × 10 (1 mark) = 20 m (1 mark).
Example 3
Explain what the gradient of a velocity-time graph represents. [2 marks]
Model answer
The gradient represents the acceleration of the object (1 mark), because acceleration is the change in velocity divided by the time taken, which is exactly what the gradient measures (1 mark).
Common mistakes
Confusing distance-time and velocity-time graphs.
On a velocity-time graph the gradient is acceleration and the area is distance.
Saying a horizontal line means stationary.
On a velocity-time graph it means constant velocity, which may not be zero.
Forgetting to halve for a triangle.
The area of a triangle is ½ × base × height.
Reading distance from the height of the line.
Distance comes from the area under the graph.
Exam tips
- Identify the graph type before interpreting anything.
- Use the gradient for acceleration and the area for distance.
- Split the area into rectangles and triangles.
- Remember horizontal means constant velocity, not stationary.
Key terms
- Velocity-time graph
- A graph of velocity against time.
- Gradient
- The steepness, giving acceleration here.
- Area under the graph
- The distance travelled.
- Uniform acceleration
- Constant acceleration, shown by a straight sloping line.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.