2.1.5—Acceleration using the gradient of a velocity–time graph

Acceleration is the tangent gradient dv/dt on a velocity–time graph. A straight segment has constant acceleration; a horizontal segment has zero acceleration.

Use signed gradients and identify the interval. A negative gradient means velocity decreases in the chosen coordinate direction, not necessarily negative speed.

A velocity falling from 10 to 4 m s⁻¹ over 3 s has average acceleration −2 m s⁻²; the tangent gives instantaneous values if the curve is non-linear.

The area under a v–t graph is displacement, while its gradient is acceleration—do not interchange them.