Velocity–Time Graphs
Slope gives acceleration and area gives displacement.
About this topic
On a velocity-time graph, the slope is acceleration and the area between the line and the time axis is displacement. A horizontal line is constant velocity, a sloped line constant acceleration, and area below the axis counts as negative displacement.
For curves, the area can be estimated by counting squares or splitting the shape into rectangles and triangles. A rectangle has area velocity times time, while a triangle uses one half base times height. The same idea becomes integration in more advanced courses.
Example: a car accelerates uniformly from 0 to 20 m/s in 10 s and then cruises at 20 m/s for 20 s. The slope in the first part is 2 m/s². The area is a triangle of 100 m plus a rectangle of 400 m, giving 500 m total displacement. Engineers analyse crash data and train timetables this way.
Common errors: a line that crosses the time axis shows a change in direction, not that the object has gone back in time. Also, a horizontal line at a nonzero value means constant velocity, not rest, which would be a line along the axis. Do not mix up the slope of a v-t graph, which is acceleration, with the slope of an x-t graph, which is velocity.
Key ideas
- Area under the curve is distance
- Slope is acceleration
- Below the axis means moving backward
Quick check
Use cases: where Velocity–Time Graphs helps
- Homework: review the key idea behind Velocity–Time Graphs before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Velocity–Time Graphs without notes.
- Visual learning: play with the interactive lab to see how Velocity–Time Graphs changes when you adjust its inputs.
- Teaching a friend: explain Velocity–Time Graphs in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Velocity–Time Graphs?
Slope gives acceleration and area gives displacement.
What will I learn in Velocity–Time Graphs?
Area under the curve is distance. Slope is acceleration. Below the axis means moving backward.
Is Velocity–Time Graphs part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Velocity–Time Graphs lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Velocity–Time Graphs?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.