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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

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.

Memory hook

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

Examples and method

Worked example

A car's velocity increases uniformly from 0 to 20 m/s in 5 s. Acceleration = 20/5 = 4 m/s². Displacement = area of triangle = 1/2 × 5 × 20 = 50 m.

Method to apply

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

Diagram support

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

How CBSE asks it

Questions may ask students to calculate acceleration from slope or displacement from rectangular, triangular, or trapezium areas.

Avoid common mistakes

Common confusion

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.

Common wrong answer

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

Exam tip

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

Quick check

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

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

Study the velocity-time graphs diagram carefully

Use the labelled diagram to keep velocity-time graphs clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of velocity-time graphs in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on velocity-time graphs.

Revision cue

Revise velocity-time graphs through the labels before writing the answer.

Answer writing and exam use

1-mark answer

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

2-mark answer

A velocity-time graph shows how velocity changes with time. Its slope gives acceleration, and the area under the graph gives displacement. Acceleration from velocity-time graph = slope = change in velocity / change in time. Displacement = area under velocity-time graph. If velocity is constant at 10 m/s for 5 s, displacement is area = 10 × 5 = 50 m.

3-mark answer

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. Acceleration from velocity-time graph = slope = change in velocity / change in time. Displacement = area under velocity-time graph. A car's velocity increases uniformly from 0 to 20 m/s in 5 s. Acceleration = 20/5 = 4 m/s². Displacement = area of triangle = 1/2 × 5 × 20 = 50 m. Questions may ask students to calculate acceleration from slope or displacement from rectangular, triangular, or trapezium areas. Saying a horizontal velocity-time line means the object is at rest is wrong unless the velocity value is zero.
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