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Velocity–time graphs
Beginner
Slope gives acceleration; area gives displacement.
On a v–t graph the slope is acceleration and the area between the curve and the axis is displacement (areas below the axis are negative). A horizontal line means constant velocity.
A triangle from 0 to 10 m/s over 5 s has area ½·5·10 = 25 m.
Crossing the time axis means the direction reverses, not that the object returns to the start.
In more detail
A velocity-time graph shows how velocity changes with time. Its slope gives acceleration, and the area under it gives displacement.
Real-world uses
- Drivers' test graphs compare acceleration over time for different cars.
- Physics labs use velocity-time graphs from motion sensors to measure acceleration directly.
- A lift's velocity-time graph shows the moment it starts moving, cruises at constant speed, then decelerates, and the area gives the height travelled.
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Frequently asked questions
What does the area under a velocity-time graph give?
The displacement. If part of the area is below the axis, it counts as negative displacement.
What does a horizontal line on a velocity-time graph mean?
Constant velocity, so zero acceleration.
Why does the area under a velocity-time graph give displacement?
Each thin strip is velocity times a small time, which is a small displacement. Adding them up gives the total displacement.
Related topics in Kinematics
Acceleration · Uniform motion · Position–time graphs · Equations of motion: v = u + at · Equations of motion: s = ut + ½at² · Equations of motion: v² = u² + 2as