Define and calculate acceleration

Calculating average acceleration

The basic formula

For rectilinear (straight-line) motion, the average acceleration is calculated as follows:

a = (v_final - v_initial) / (t_final - t_initial) = delta_v / delta_t

where:

a is the average acceleration (in m/s²)
v_final and v_initial are the velocities in m/s
delta_t is the elapsed time in seconds (s)

Practical example

A cyclist is cycling at 5 m/s. He starts pedalling hard and reaches 15 m/s in 4 seconds. Let’s calculate his average acceleration:

a = (15 - 5) / 4 = 10 / 4 = 2.5 m/s²

This means that, on average, his speed increases by 2.5 m/s every second.

Braking scenario

If a motorbike is travelling at 24 m/s, then brakes and comes to a stop in 6 s:

a = (0 – 24) / 6 = –4 m/s²

The negative sign indicates that the acceleration vector is opposite to the direction of motion: this is deceleration.

A common pitfall to avoid

Do not confuse speed with acceleration! A high speed does not necessarily mean high acceleration: a high-speed train travelling at 300 km/h in a straight line at a constant speed has zero acceleration, whereas a small car pulling away has significant acceleration even if its speed remains low.

Key points to remember