# Acceleration

Acceleration is the rate of change in speed (or velocity).

It is defined as follows:

$acceleration = \frac{{final\,speed - initial\,speed}}{{time\,taken}}$

In physics, the following standard symbols are used to represent the quantities shown in the acceleration equation:

• $$u$$
• $$v$$
• $$a$$
• $$t$$ -

With these symbols, the relationship for acceleration can be rewritten as:

$a = \frac{{v - u}}{t}$

The formula is commonly rearranged as:

$v = u + at$

to give the final speed $$v$$ of an object after it has accelerated.

Acceleration is measured in metres per second per second ($$m\,s^{-2}$$), often pronounced as 'metres per second squared'.

Sometimes when we are describing motion we use the term 'constant speed'.

An object is travelling at a constant speed when its instantaneous speed has the same value throughout its journey. For example, if a car is travelling at a constant speed the reading on the car's speedometer does not change. The speedometer displays the speed of the car at each moment in time throughout the car's journey. In cases like this, where the motion involves only constant speed, the instantaneous speed of the object can be worked out using the relationship:

$speed = \frac{{distance\,travelled}}{{time\,taken}}$

We also sometimes refer to a moving object as having a 'constant acceleration' or a 'uniform acceleration'. A constant or uniform acceleration means that the speed of the object changes by the same amount every second.

When the speed of an object is decreasing with time (ie slowing down), the object's speed is changing and so, by definition, the object is accelerating. If the of an object is decreasing, the acceleration calculated will be negative.

This is sometimes known as a .