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Motion · 12 min

Motion graphs

Graphs make stops, steady motion and changing motion visible. The axis labels determine what a slope or area means.

01Why this matters

Graphs make stops, steady motion and changing motion visible. The axis labels determine what a slope or area means.

02See it

time (s)048velocity (m/s)
The triangular area under the velocity–time line is ½ × 4 × 8 = 16 metres.
t = 0, v = 0t = 4 s, v = 8slope = 2 m/s²area = 16 m
Read left to right: t = 0, v = 0 → t = 4 s, v = 8 → slope = 2 m/s² → area = 16 m. Each panel connects one part of the example.

03Understand it

A motion graph shows how a quantity such as position or velocity changes with time.

On a position-time graph, gradient is velocity. A horizontal segment means position is unchanged. On a velocity-time graph, gradient is acceleration and signed area gives displacement. A horizontal velocity-time segment means constant velocity, which may be non-zero.

04Guided example

A velocity-time graph rises linearly from 0 m/s to 8 m/s over 4 s. Find acceleration and displacement.

  1. Gradient is rise/run: (8 − 0)/(4 − 0) = 2 m/s².
  2. The region under the line is a triangle with base 4 s and height 8 m/s.
  3. Its area is ½ × 4 × 8 = 16 m. This is displacement; motion stays positive, so distance is also 16 m.

05Try it

A velocity-time line stays at 3 m/s for 5 s. Displacement?
A little hint

Find the area of the rectangle.

06Practise it

Velocity rises from 0 to 6 m/s in 3 s. Gradient?
A little hint

Rise divided by run.

The same triangular graph: displacement?
A little hint

Triangle area is half base times height.

07Use it in the real world

A flat line at 6 m/s lasting 10 s on a velocity-time graph represents a displacement of 6 × 10 = 60 m.

Go a little deeper

Area below zero on a velocity-time graph contributes negative displacement. For total distance, add the magnitudes of those areas instead.

08Quick check

A position-time graph is horizontal. Velocity?
A little hint

A horizontal line has zero gradient.

09Summary

A motion graph shows how a quantity such as position or velocity changes with time. Its area is ½ × 4 × 8 = 16 m. This is displacement; motion stays positive, so distance is also 16 m.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

displacement = signed area under velocity–time graph

Time in s and velocity in m/s give area in m. Gradient has units m/s².

constant velocity: Δx = vt

Find this in the formula library →