Two objects can have the same acceleration and still travel different distances in the same time. Acceleration is the gradient of a velocity–time graph. Displacement is the signed area under it.
If both objects move in the positive direction throughout, displacement equals distance travelled. The object with the higher starting velocity can cover more distance even when both velocities increase at the same rate.
- Find each gradient from the change in velocity divided by time.
- Calculate each area over the same time interval.
- Check whether velocity stays positive before calling the area a distance.
Worked example | Same gradient, different starting velocities
Over four seconds, object A increases uniformly from 2 m/s to 10 m/s and B increases uniformly from 6 m/s to 14 m/s. Each velocity rises by 8 m/s, so both accelerations are 8 ÷ 4 = 2 m/s².
The graph for A encloses a trapezium with area ½(2 + 10) × 4 = 24 m. The graph for B gives ½(6 + 14) × 4 = 40 m. Both velocities are positive, so B travels 16 m farther during the interval.
Find the difference without calculating both areas
At every instant, B moves 4 m/s faster than A. The two graph lines stay 4 m/s apart. The area between them is 4 m/s × 4 s = 16 m. This is the difference in displacement.
Compare two objects over three seconds
Object P increases uniformly from 3 m/s to 9 m/s. Over the same three seconds, Q increases uniformly from 5 m/s to 11 m/s. Find their acceleration and the difference in distance travelled.
Answer. Both have acceleration 6 ÷ 3 = 2 m/s². Q stays 2 m/s faster for three seconds, so it travels 6 m farther.
Frequently asked questions
Does the higher graph always have the larger displacement over the same interval?
If one velocity stays above the other throughout, it contributes the larger signed area over that interval.
What if velocity becomes negative?
Below-axis area counts negatively for displacement. For distance, add the magnitudes of the areas on both sides of the axis.
Official information
SEAB, 2027 SEC G3 Physics syllabus (K323), Kinematics, velocity–time graphs and displacement. Syllabus checked 11 November 2026. The examples are original.