Worked examples

Example 1. A straight line on a displacement–time graph passes through (t = 2 s, d = 10 m) and (t = 8 s, d = 40 m). Velocity = slope = (40 − 10)/(8 − 2) = 30/6 = 5 m/s.

Example 2. A curved d–t graph: at t = 1 s the object is at 1 m and at t = 5 s it is at 25 m. The average velocity between these moments is (25 − 1)/(5 − 1) = 6 m/s. The instantaneous velocity at t = 3 s needs a tangent drawn at t = 3 s; if the tangent rises 12 m in 2 s, the instantaneous velocity is 6 m/s.

Example 3 (graph in words). A walker moves from the origin for 10 s, rising to 20 m; then the graph is horizontal for 5 s; then it goes back down to 0 at t = 25 s. Velocities: first stage 20/10 = +2 m/s; second stage 0 (rest); third stage (0 − 20)/10 = −2 m/s (returning). The total displacement at the end is zero, though the distance covered is 40 m.