"Whoa, you really went from zero to sixty there!"

Have you ever heard someone use the idiom "zero to sixty" like I did in the above example? When someone says something went from "zero to sixty," they’re really saying that things accelerated very quickly. **Acceleration is the amount by which the velocity of something changes over a set period of time.**

In this article, we’ll be talking all about acceleration: what it is and how to calculate it. Buckle up!

## What Is Acceleration?

**Acceleration is the rate of change of velocity over a set period of time.** You need to have both velocity and time to calculate acceleration.

Many people confuse acceleration with velocity (or speed). First of all, velocity is simply speed with a direction, so the two are often used interchangeably, even though they have slight differences. **Acceleration is the rate of change of velocity, meaning something is getting faster or slower.**

## What Is the Acceleration Formula?

You can use the acceleration equation to calculate acceleration. Here is the most common acceleration formula:

$$a = {Δv}/{Δt}$$

where $Δv$ is the change in velocity and $Δt$ is the change in time.

You can also write the acceleration equation like this:

$$a = {v(f) - v(i)}/{t(f) - t(i)}$$

In this acceleration equation, $v(f)$ is the final velocity while is the $v(i)$ initial velocity. $T(f)$ is the final time and $t(i)$ is the initial time.

Some other things to keep in mind when using the acceleration equation:

**You need to subtract the initial velocity from the final velocity.**If you reverse them, you will get the direction of your acceleration wrong.

- If you don’t have a starting time, you can use “0”.

- If the final velocity is less than the initial velocity, the acceleration will be negative, meaning that the object slowed down.

Now let’s breakdown the acceleration equation step-by-step in a real example.

## How to Calculate Acceleration: Step-by-Step Breakdown

Now we’ll breakdown the acceleration formula step-by-step using a real example.

A race car accelerates from 15 m/s to 35 m/s in 3 seconds. What is its average acceleration?

First, write the acceleration equation.

$$a = {v(f) - v(i)}/{t(f) - t(i)}$$

Next, define your variables.

$a$ = what we are solving for

$$V(f) = 35 m/s$$

$$V(i) = 15 m/s$$

$$T(f) = 3 s$$

$$T(i) = 0 s$$

Now, plug your variables into the equation and solve:

$$A = {{(35 - 15)m}/{s}/{(3 - 0)s}$$

$$A = {(35 - 15)}/{(3 - 0)} m/s^2$$

$$A = {20/3} m/s^2$$

$$A = 6.66 m/s^2$$

Let’s try another example.

A cyclist traveling at 23.2 m/s comes to a complete stop in 1.5 $s$. What was her deceleration?

First, write the acceleration equation.

$$a = (v(f) - v(i)) ÷ (t(f) - t(i))$$

Next, define your variables.

a = what we are solving for

$$V(f) = 0 m/s$$

$$V(i) = 23.2 m/s$$

$$T(f) = 1.4 s$$

$$T(i) = 0 s$$

Now, plug your variables into the equation and solve:

$$A ={{(0 - 23.2)m}/s}/{(1.4 - 0)s}$$

$$A = {0 - 23.2}/{1.4 - 0} m/s^2$$

$$A = -23.2/1.4 m/s^2$$

$$A = -16.57 m/{s^2}$$

## 2 Other Common Acceleration Formulas

Wondering how to calculate acceleration using a different formula? There are several other common acceleration formulas.

### Angular Acceleration Formula

**Angular acceleration is the rate at which the angular acceleration of a rotating object changes with respect to time.**

Here is the angular acceleration equation:

$$a = {\change \in \angular \velocity}/{\change \in \time}$$

### Centripetal Acceleration Formula

**Centripetal acceleration is the rate of motion of an object inwards towards the center of a circle.**

Here is the centripetal acceleration equation:

$$a(c) = {v^2}/r$$

$a(c) $= acceleration, centripetal

$v$ = velocity

$r$ = radius

## Key Takeaways

Acceleration is the rate of change of velocity over a set period of time.

You calculate acceleration by dividing the change in velocity by the change in time.

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