Velocity-Time Graphs
Simple Explanation
A velocity-time graph plots an object's velocity against time. The slope of the line gives the acceleration, and the area between the line and the time axis gives the total displacement over that time.
Why Do We Need It?
A single graph like this can show you an object's acceleration AND how far it travelled, just by reading its slope and the area underneath it.
See It
A velocity-time graph with two draggable points and a live acceleration readout equal to the slope of the line between them
Worked Example
Find acceleration from a velocity-time graph
A velocity-time graph shows a straight line from (0 s, 5 m/s) to (10 s, 25 m/s). Find the acceleration.
Why Does This Work?
Slope is 'change in y divided by change in x' — on a velocity-time graph that is exactly 'change in velocity divided by change in time,' the definition of acceleration.
Real-Life Example
Analyzing a rocket launch
Engineers plot a rocket's velocity-time graph during launch.
The slope at any point gives its acceleration, and the area under the curve up to any time gives exactly how far it has travelled — both read straight off the same graph.
Practice
A velocity-time graph shows a straight line from (0 s, 0 m/s) to (4 s, 20 m/s). What is the acceleration?
MediumCommon mistake
Confusing a distance-time graph's slope (speed) with a velocity-time graph's slope (acceleration) — they look similar but represent completely different quantities.
Quick Review
- The slope of a velocity-time graph equals acceleration.
- The area under a velocity-time graph equals displacement.
- A flat line means constant velocity (zero acceleration).