medium difficulty5 min

Position-Time Graphs

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

In one line: On a position-time graph, slope speaks.

Practice This Concept

Understand it

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.

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.

See it worked out

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

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 you can reuse

1Read two clear points from the graph.
2Find change in position and change in time.
3Divide change in position by change in time.
4Use the slope shape to describe the motion.

Sketch it in your answer

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.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

Common wrong answer

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

Don't mix this up

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

Exam tip

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