2.1.4—Velocity using the gradient of a displacement–time graph

The tangent gradient ds/dt at a point on an s–t graph is velocity. A secant gradient over an interval is average velocity.

Read the sign from the slope and compare steepness for speed. A horizontal tangent means instantaneous velocity zero, not necessarily no future motion.

For s=t², the tangent gradient at t=3 is 6 m s⁻¹, while the average velocity from t=2 to 3 is 5 m s⁻¹.

The height of an s–t graph is position; velocity is its gradient.