Intermediate · 11 min
Reading motion graphs
Use graph gradients and areas to connect displacement, velocity, and acceleration.
The slope describes a rate
A displacement–time graph shows position relative to a chosen starting point. Its gradient is velocity: change in displacement divided by change in time. A straight rising line represents constant positive velocity; a horizontal line represents rest. A falling line represents negative velocity, not necessarily slowing down. For a curved graph, a tangent gives the velocity at one instant.
Worked example
Displacement changes from 4 m to 16 m between 1 s and 5 s. Average velocity = (16 − 4) ÷ (5 − 1) = 3 m/s
Area gives displacement
On a velocity–time graph, gradient is acceleration and signed area between the graph and the time axis is displacement. Area below the time axis counts as negative displacement. For distance travelled, add the magnitudes of the areas instead. Rectangles and triangles let you calculate areas without calculus when velocity is constant or changes uniformly.
Worked example
Velocity increases uniformly from 0 to 6 m/s over 4 s. Displacement = triangle area = ½ × 4 × 6 = 12 m
Compare two graphs
- Draw a velocity–time graph for 4 m/s over 5 s and calculate its area.
- Draw a second graph rising uniformly from 0 to 8 m/s over 5 s. Compare the displacements and explain the difference in motion.