# Acceleration

Acceleration is how fast velocity changes:

- Speeding up
- Slowing down (also called
*deceleration*) - Changing direction
- etc

It is usually shown as:

**m/s ^{2}**

*"meters per second squared"*

What is this "**per second squared**" thing? An example will help:

### A runner accelerates from **5 m/s** (5 meters per second) to **6 m/s** *in just one second*

So they accelerate by 1 meter per second **per second**

See how "per second" is used twice?

It can be thought of as (m/s)/s but is usually written m/s^{2}

So their acceleration is **1 m/s ^{2}**

The formula is:

Acceleration = \frac{Change in Velocity (m/s)}{Time (s)}

### Example: A bike race!

You are cruising along in a bike race, going a steady **10 meters per second** (10 m/s).

**Acceleration**: Now you start cycling faster! You increase to **14 m/s** over the next 2 seconds (still heading in the same direction):

Your velocity **increases by 4 m/s**, over a time period of **2 seconds**, so:

Acceleration = \frac{Change in Velocity (m/s)}{Time (s)}

= \frac{4 m/s}{2 s} = 2 m/s^{2}

Your speed changes by **2 meters per second** *per second*.

### Example: You are running at 7 m/s, and skid to a halt in 2 seconds.

You went from 7 m/s to 0, so that is a decrease in speed:

Acceleration = \frac{Change in Velocity (m/s)}{Time (s)}

= \frac{−7 m/s}{2 s} = −3.5 m/s^{2}

We don't always say it, but acceleration has **direction** (making it a vector):

### A car is heading **West at 16 m/s**.

The driver flicks the wheel, and within 4 seconds has the car headed **East at 16 m/s**.
What is the acceleration?

The numbers are the same, but the direction is different!

Acceleration = \frac{Change in Velocity (m/s)}{Time (s)}

Acceleration = \frac{From 16 m/s West to 16 m/s East}{4 s}

From 16 m/s West to 16 m/s East is a total change of 32 m/s towards the East.

Acceleration = \frac{32 m/s East}{4 s} = 8 m/s^{2} East

For more complicated direction changes read vectors.