medium difficulty7 min

Velocity-Time Graphs

A velocity-time graph shows how velocity changes with time. Its slope gives acceleration, and the area under the graph gives displacement.

In one line: Velocity-time graph: slope for acceleration, area for displacement.

Practice This Concept

Understand it

A horizontal line on a velocity-time graph means constant velocity and zero acceleration. A straight sloping line means uniform acceleration. The area between the graph and time axis represents displacement during that time interval.

Example

If velocity is constant at 10 m/s for 5 s, displacement is area = 10 × 5 = 50 m.

Rule to remember

Acceleration from velocity-time graph = slope = change in velocity / change in time.

Displacement = area under velocity-time graph.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A car's velocity increases uniformly from 0 to 20 m/s in 5 s.

1Acceleration = 20/5 = 4 m/s².
2Displacement = area of triangle = 1/2 × 5 × 20 = 50 m.

Method you can reuse

1For acceleration, take two points and calculate slope.
2For displacement, identify the shape under the graph, calculate its area, and attach the correct unit metre.

Sketch it in your answer

Draw time on the x-axis and velocity on the y-axis. Use rectangle and triangle areas for displacement in simple cases.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What does the area under a velocity-time graph represent?

Think first, then show answer

The area under a velocity-time graph represents displacement, because velocity multiplied by time gives displacement.

Common wrong answer

Saying a horizontal velocity-time line means the object is at rest is wrong unless the velocity value is zero.

Don't mix this up

Students often confuse velocity-time graphs with position-time graphs and say a horizontal line means rest. In a velocity-time graph, horizontal line means constant velocity, not necessarily rest.

Exam tip

First identify the graph type. In velocity-time graphs, slope gives acceleration and area gives displacement.