Definition and equation
- Acceleration is the rate of change of velocity, that is, how much the velocity changes each second
- Equation:
a = Δv / t = (v − u) / t
- where:
- a = acceleration in metres per second squared (m/s²)
- u = initial velocity (m/s)
- v = final velocity (m/s)
- t = time over which the velocity changes (s)
- The units of acceleration, m/s², come from "change in m/s, per s", because the velocity changes by a metres per second every second
Sign of the acceleration
- If the calculated value of a comes out positive, the object is gaining speed in the direction it is already moving (it is accelerating)
- If the calculated value of a comes out negative, the object is losing speed; this is called a deceleration
- The sign therefore carries physical meaning, because a minus sign in front of an acceleration is the maths telling you the motion is slowing
Example — a bullet train slows steadily from 60 m/s to 45 m/s in 20 s. Calculate its acceleration and state whether it is speeding up or slowing down.
- Δv = v − u = 45 − 60 = −15 m/s
- a = Δv / t = −15 / 20 = −0.75 m/s²
- The acceleration is negative, so the train is decelerating (slowing down)