The idea
A horizontal displacement–time line means the object is stationary. A horizontal velocity–time line means constant velocity. On a curved displacement–time graph, the gradient of a tangent gives instantaneous velocity. Area below the time axis on a velocity–time graph contributes negative displacement; use the magnitudes of the areas to calculate total distance.
Worked example
Velocity rises uniformly from 0 to 8 m/s in 4 s, then stays at 8 m/s for 3 s. Find the displacement.
- The first area is a triangle: ½ × 4 × 8 = 16 m.
- The second area is a rectangle: 3 × 8 = 24 m.
- Total displacement = 16 + 24 = 40 m. The initial acceleration is 8 ÷ 4 = 2 m/s².
A mistake to avoid
The height of a velocity–time graph is velocity, not acceleration. Acceleration comes from its gradient.
Check your understanding
A velocity–time graph stays at −3 m/s for 6 s. Find displacement and distance.
Show the explanation
Displacement = −3 × 6 = −18 m. Distance is 18 m because there is no change of direction.
Explore the lesson
This guide connects to Reading the Story of Motion in the IB Physics course. The first two published lessons per subject are free previews; further interactive lessons require an account.