AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER
Distance–time graphs
Forces · Lesson 11 of 20
Warm-up
Answer each one, then check.
1. What is the gradient of a graph?
Change in y divided by change in x
2. What does a horizontal line on a distance-time graph mean?
The object is stationary
3. What is speed?
Distance divided by time
4. What is acceleration?
Rate of change of velocity
5. What does a steeper line mean?
A faster speed
Learning Objectives
1. Draw distance–time graphs from measurements.
2. Interpret lines and slopes of distance–time graphs.
3. Calculate speed from the gradient of a distance–time graph.
4. Find the speed of an accelerating object at an instant using a tangent (Higher tier).
Distance–Time Graphs
The gradient of a distance–time graph is the speed of the object.
A straight line means constant speed, a horizontal line means stationary, and a curve means the speed is changing.
Reading a Distance–Time Graph
|
Gradient = change in distance ÷ change in time. |
A distance-time graph with constant speed, stationary and returning sections, and a gradient triangle.
What the Graph Shows
Learn these.
|
Shape |
Meaning |
|---|---|
|
Straight line sloping up |
Constant speed |
|
Horizontal line |
Stationary |
|
Steeper line |
Higher speed |
|
Curve getting steeper |
Accelerating |
|
Curve getting shallower |
Decelerating |
Speed from a Gradient
|
An object travels 40 m in the first 20 s. Calculate its speed from the graph. |
1. Gradient
(change in distance)/(change in time)
2. Substitute
40/20
3. Answer
2.0 m/s
Answer: 2.0 m/s
Describing a Journey
|
Describe the motion shown from 20 s to 40 s where the line is horizontal. |
1. Distance
Does not change
2. Speed
Zero
Answer: The object is stationary.
Tangent (Higher)
|
The distance is given by s = 0.5t² (in metres, t in seconds). Find the speed at t = 6 s using a tangent. |
1. Draw a tangent
Touching the curve at t = 6 s
2. Gradient of the tangent
Δs/Δt from two points on the tangent: about 6 m/s
3. Check
The speed is t = 6 m/s from s = 0.5t²
Answer: About 6 m/s.
Drawing Graphs
Good practice.
▸ Axes. Time on the x-axis, distance on the y-axis, with units.
▸ Points. Plot from a table, then join with a ruler (or a smooth curve if the speed changes).
▸ Gradient. Use a large triangle for accuracy.
▸ Units. m/s if distance in m and time in s.
Key Terms
|
Distance–time graph A graph of distance against time. |
Gradient How steep a line is. |
|
Stationary Not moving. |
Tangent A straight line that touches a curve at one point. |
|
Constant speed The same speed all the time. |
Accelerating Speeding up. |
Your Task: Story Graph
12 minutes
|
A cyclist travels 100 m in 20 s, stops for 20 s and then travels 60 m in 20 s. Sketch the graph and calculate the speed in each part. 1. Plot the three sections. 2. Gradient for each. |
A good answer shows: Part 1: 5.0 m/s. Part 2: 0 m/s. Part 3: 3.0 m/s.
Can I...?
☐ Draw a distance–time graph.
☐ Say what a horizontal line means.
☐ Calculate speed from a gradient.
☐ Compare speeds from slopes.
☐ Describe a journey.
☐ Describe a curve.
☐ Draw a tangent.
☐ Use units.
Summary
✓ Gradient = speed.
✓ Horizontal line = stationary.
✓ Steeper = faster.
✓ Higher: tangent to a curve gives instantaneous speed.
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EXAM FOCUS The graph shows 100 m in 20 s. Calculate the speed in the first 20 s. (2 marks) Gradient = distance ÷ time. |