Speed-Time Graphs
A speed-time graph plots speed against time, where gradient shows acceleration and area underneath shows distance.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
A speed-time graph plots speed against time, where gradient shows acceleration and area underneath shows distance.
- Positive slope is acceleration
- The area under the graph is distance travelled
- A flat line is constant speed
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Speed-Time Graphs?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Speed-Time Graphs. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Speed-Time Graphs in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Speed-Time Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Speed-Time Graphs in detail
A speed-time graph plots speed against time. Its gradient gives acceleration, so a horizontal line means constant speed, an upward slope means speeding up and a downward slope means slowing down. A steeper slope means larger acceleration or deceleration.
The area under the graph represents the distance travelled, which can be found by splitting it into triangles, rectangles and trapezia. Estimating areas under curves gives approximate distance when speed changes smoothly. Be careful to distinguish these graphs from distance-time graphs, where a horizontal line means stopped.
How the interactive helps you understand Speed-Time Graphs
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Speed-Time Graphs.
Real-life uses and examples
- Spot Speed-Time Graphs in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Speed-Time Graphs by estimating first, then working it out step by step.
- Use Speed-Time Graphs when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Speed-Time Graphs.
- Memorising the steps for Speed-Time Graphs without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Speed-Time Graphs
What is Speed-Time Graphs?
A speed-time graph plots speed against time, where gradient shows acceleration and area underneath shows distance.
What are the most important points about Speed-Time Graphs?
The main points are: Positive slope is acceleration; The area under the graph is distance travelled; A flat line is constant speed.
Why is Speed-Time Graphs useful?
Understanding Speed-Time Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Speed-Time Graphs?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Speed-Time Graphs?
Related topics in Mathematics include Angles on Lines and Points, Types of Triangle, Congruence.