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Position-Time Graphs

A position-time graph shows how the position of an object changes with time. The slope of the graph gives velocity.

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Student-friendly explanation

A horizontal line means position is not changing, so the object is at rest. A straight sloping line means uniform velocity. A steeper slope means greater velocity. A curved line shows changing velocity, which indicates non-uniform motion.

How to write this in exams

  1. 1

    Start with the exact idea

    A position-time graph shows how the position of an object changes with time. The slope of the graph gives velocity.

  2. 2

    Then show how to use it

    Read two clear points from the graph. Find change in position and change in time. Divide change in position by change in time. Use the slope shape to describe the motion.

  3. 3

    Add one concrete example

    If position increases by 20 m in 10 s on a straight graph, velocity is 2 m/s.

  4. 4

    Avoid this incomplete answer

    Choosing the line that is highest on the graph as fastest is wrong unless its slope is also greatest.

Definition

A position-time graph shows how the position of an object changes with time. The slope of the graph gives velocity.

Example

If position increases by 20 m in 10 s on a straight graph, velocity is 2 m/s.

Rule to remember

Velocity from position-time graph = slope = change in position / change in time.

Memory hook

On a position-time graph, slope speaks.

Examples and method

Worked example

If a graph goes from position 10 m at 2 s to position 30 m at 6 s, velocity = (30 - 10)/(6 - 2) = 20/4 = 5 m/s.

Method to apply

Read two clear points from the graph. Find change in position and change in time. Divide change in position by change in time. Use the slope shape to describe the motion.

Diagram support

Draw time on the x-axis and position on the y-axis. Use horizontal, straight sloping, and curved lines to compare rest, uniform motion, and changing motion.

How CBSE asks it

Students may be asked to identify rest, compare speeds from slopes, or calculate velocity using two points on a graph.

Avoid common mistakes

Common confusion

Students sometimes read height of the graph as speed, but velocity is shown by slope, not by how high the line is.

Common wrong answer

Choosing the line that is highest on the graph as fastest is wrong unless its slope is also greatest.

Exam tip

For graph questions, always look at slope first: flat means rest, straight slope means uniform velocity, changing slope means changing velocity.

Quick check

What does a horizontal line on a position-time graph show?

A horizontal line shows that position is constant with time, so the object is at rest with respect to the chosen reference point.

Study the position-time graphs diagram carefully

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

What this diagram makes clear

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

Where this helps in exams

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

Revision cue

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

Answer writing and exam use

1-mark answer

A position-time graph shows how the position of an object changes with time. The slope of the graph gives velocity.

2-mark answer

A position-time graph shows how the position of an object changes with time. The slope of the graph gives velocity. Velocity from position-time graph = slope = change in position / change in time. If position increases by 20 m in 10 s on a straight graph, velocity is 2 m/s.

3-mark answer

A horizontal line means position is not changing, so the object is at rest. A straight sloping line means uniform velocity. A steeper slope means greater velocity. A curved line shows changing velocity, which indicates non-uniform motion. Velocity from position-time graph = slope = change in position / change in time. If a graph goes from position 10 m at 2 s to position 30 m at 6 s, velocity = (30 - 10)/(6 - 2) = 20/4 = 5 m/s. Students may be asked to identify rest, compare speeds from slopes, or calculate velocity using two points on a graph. Choosing the line that is highest on the graph as fastest is wrong unless its slope is also greatest.
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