GCSE MATHS • HIGHER TIER
Speed-Time Graphs Made Simple
Read speed-time graphs, recognise acceleration and deceleration, calculate distance from area and acceleration from gradient.
Clear method
Exam practice
Worked proofs
Speed-Time Graphs in Four Moves
1
Read
Check the time and speed axes, scales and units.
2
Interpret
Identify acceleration, constant speed or deceleration.
3
Calculate
Use area for distance and gradient for acceleration.
4
Check
Include correct units and relate the answer to the journey.
What You’ll Learn
Read Speed-Time Graphs
Find the speed of an object at a given time.
Interpret Slopes
Recognise acceleration, deceleration and constant speed.
Calculate Distance
Use the area under the graph to find distance travelled.
Calculate Acceleration
Use change in speed ÷ time taken.
Compare Motion Graphs
Distinguish speed-time graphs from distance-time graphs.
Key Rules
Distance-time graph:
Gradient = speed
Speed-time graph:
Gradient = acceleration
Worked Proof: Speed-Time Graphs
Real-Life Applications
Speed-time graphs are used in transport planning, motorsport, aviation, athletics, engineering and scientific research. They help people understand how objects move, how quickly they speed up and how far they travel over time.
More Worked Examples
1
An object travels at 20 m/s for 5 seconds. Calculate the distance travelled.
Distance = Speed×Time
= 20×5
=100 m
=100 m
2
A speed-time graph forms a triangle with a base of 8 seconds and a height of 10 m/s. Calculate the distance travelled.
Distance = Area under the graph
Area of triangle = 1/2 × Base × Height
= 1/2 × 8 × 10
=40 m
= 1/2 × 8 × 10
=40 m
3
A speed-time graph falls from 30 m/s to 10 m/s.
Change in speed = Final speed−Initial speed
= 30-10
= 20 m/s
The negative change means the speed has decreased by 20 m/s.
= 20 m/s
The negative change means the speed has decreased by 20 m/s.
4
After 4 seconds, the graph shows a speed of 12 m/s.
(Time,Speed) = (4,12)
t = 4 s
v = 12 m/s
v = 12 m/s
- Common GCSE Mistakes
- Graph type: Do not confuse speed-time graphs with distance-time graphs.
- Area: Remember the area under a speed-time graph gives distance.
- Gradient: Remember the gradient of a speed-time graph gives acceleration.
- Units: Check and include the correct units.
- Horizontal line: It means constant speed, not stationary, unless it lies on the time axis.
- Area arithmetic: Calculate rectangles, triangles and trapeziums carefully.
- Exam Tips
- Check axes and units before reading the graph.
- Upward slope = acceleration; downward slope = deceleration.
- Horizontal above zero = constant speed.
- Use area under the graph to calculate distance.
- Use gradient to calculate acceleration.
- Keep distance-time and speed-time graph rules separate.
Skills Used in Speed-Time Graphs
Graph Interpretation
Speed and Time
Acceleration
Gradient
Area of Rectangles
Area of Triangles
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Speed-Time Graphs Tutorial
Step-by-step walkthroughs of Speed-Time Graphs with clear methods and exam tips.
Frequently Asked Questions
It shows how the speed of an object changes over time.
It means the object is accelerating.
It means the object is decelerating.
It means constant speed unless the line is on the time axis, where the speed is zero.
It represents distance travelled.
The gradient represents acceleration.
Acceleration = change in speed ÷ time taken.