17 Worked examples
Example 1. A car increases its velocity uniformly from 10 m/s to 30 m/s in 8 s. a = (30 − 10)/8 = +2.5 m/s².
Example 2 — braking. A car moving at 25 m/s brakes uniformly and its velocity falls to 5 m/s in 4 s. a = (5 − 25)/4 = −5 m/s² (deceleration of 5 m/s²).
Example 3 — time to reach a velocity. A motorcycle starts from rest with a = 3 m/s². Time to reach 90 km/h (= 25 m/s)? From a = Δv/Δt: t = 25/3 = 8.3 s.
✍️ Worked examples
Example 4 — a ball thrown up (sign meaning). Take upward as positive: a ball leaves the hand at +20 m/s and, because it slows down, has a negative acceleration (−10 m/s²); after 1 s the velocity is +10 m/s, after 2 s it is 0, and after 3 s it is −10 m/s (moving down, now speeding up because velocity and acceleration are both negative).