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Motion graphs: distance–time and velocity–time journeys

Build a three-stage journey to compare the distance–time graph (where gradient = speed, estimated on a curve by drawing a tangent) with the velocity–time graph (where gradient = acceleration and area = distance).

Distance–time graph (gradient of tangent at P = instantaneous speed)

Velocity–time graph (gradient = acceleration, shaded area = distance)

Tangent on the curved distance–time graph (drag P or adjust below)

Time t at point P on the journey t = 2.0 s

Drawn line gradient at P (practise matching the tangent) 6.0 m/s (exact tangent)

Motion graphs: distance–time and velocity–time journeys

Distance–time graph (gradient of tangent at P = instantaneous speed)

Velocity–time graph (gradient = acceleration, shaded area = distance)

Tangent on the curved distance–time graph (drag P or adjust below)

Build the 3 journey stages (starts from rest v₀ = 0 m/s)

Stage-by-stage breakdown (acceleration & trapezium/triangle area)