Distance–Time Graphs
Revise Distance–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 distance–time graph the gradient gives the speed, and a curved line shows that the speed is changing.
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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 distance-time graph shows how the distance travelled by an object varies with time. The gradient of the line gives the speed.
A horizontal line means the object is stationary, because the distance is not changing. A straight sloping line means constant speed, and the steeper the line the faster the object is moving.
A curved line means the speed is changing, so the object is accelerating or decelerating. To find the speed at a particular moment on a curve, draw a tangent to the curve at that point and calculate its gradient.
Revision notes
Reading the graph
The gradient of a distance-time graph gives the speed.
A horizontal line means the object is stationary. A straight sloping line means constant speed. A steeper line means a greater speed.
Curved lines
A curved line means the speed is changing.
A line curving upwards and getting steeper shows acceleration. A line curving and becoming less steep shows deceleration.
Finding speed on a curve
Draw a tangent to the curve at the point of interest and calculate the gradient of that tangent.
Use two points far apart on the tangent for accuracy, and leave the tangent drawn on the graph so the method marks are available.
Key points
- The gradient gives the speed.
- A horizontal line means stationary.
- A straight sloping line means constant speed.
- A steeper line means a greater speed.
- A curved line means changing speed.
- Draw a tangent to find the speed on a curve.
Worked examples
Example 1
A distance-time graph shows a horizontal line. Describe the motion. [2 marks]
Model answer
The object is stationary (1 mark), because the distance is not changing as time passes (1 mark).
Example 2
An object travels 60 m in 12 s at constant speed. Calculate the gradient of its distance-time graph and state what it represents. [3 marks]
Model answer
Gradient = change in distance ÷ change in time = 60 ÷ 12 (1 mark) = 5 (1 mark). The gradient represents the speed, so the speed is 5 m/s (1 mark).
Example 3
Explain how to find the speed of an object at a particular moment from a curved distance-time graph. [2 marks]
Model answer
Draw a tangent to the curve at that point (1 mark) and calculate the gradient of the tangent, which gives the speed at that instant (1 mark).
Common mistakes
Saying a horizontal line means constant speed.
It means stationary — the distance is not changing.
Reading the speed from the height of the line.
Speed comes from the gradient, not the value on the axis.
Using a chord instead of a tangent.
A tangent gives the speed at a moment; a chord gives an average.
Not leaving the tangent on the graph.
Method marks require the tangent to be visible.
Exam tips
- Use the gradient, never the height, for speed.
- Remember horizontal means stationary.
- Draw and leave a tangent for instantaneous speed.
- Describe the motion in words as well as numbers.
Key terms
- Distance-time graph
- A graph of distance against time.
- Gradient
- The steepness of a line, giving the speed here.
- Tangent
- A line touching a curve at one point.
- Stationary
- Not moving, shown by a horizontal line.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.