# Acceleration

You can calculate the of an object from its change in velocity and the time taken.

Velocity is not exactly the same as speed. Velocity has a direction as well as a speed. For example, 15 m/s is a speed, but 15 m/s North is a velocity (North is the direction).

Commonly velocities are + (which means forwards) or - (which means backwards).

For example, -15 m/s means moving backwards at 15 metres every second.

## The equation

When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes.

$\text{acceleration (metre per second squared)} = \frac{change~in~velocity~(metre~per~ second)}{time~taken~ (second,~s)}$

The units for acceleration are commonly written as m/s/s or m/s2. The equation for acceleration can also be represented as:

$a = (v-u) \div t$

where:

a is acceleration in m/s/s or m/s2

v is final velocity in m/s

u is initial velocity in m/s

t is time in s

For example, a car accelerates in 5 s from 25 m/s to 3 5m/s. Its velocity changes by 35 - 25 = 10 m/s. Therefore its acceleration is 10 ÷ 5 = 2 m/s2

Deceleration, or negative acceleration, is observed when an object slows down. The units are the same as for acceleration but the number has a negative symbol before it. For example, the car slowed down at -1 m/s2.

Here’s another worked example. This time a car decelerates in 5 s from 35 m/s to 25 m/s. Its velocity changes by 25 - 35 = -10 m/s. Therefore its acceleration is -10 ÷ 5 = -2 m/s2

A summary of speed, distance and velocity