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How to Calculate Acceleration: The 3 Formulas You Need

Posted by Hayley Milliman | May 2, 2019 1:00:00 PM

General Education



"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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Hayley Milliman
About the Author

Hayley Milliman is a former teacher turned writer who blogs about education, history, and technology. When she was a teacher, Hayley's students regularly scored in the 99th percentile thanks to her passion for making topics digestible and accessible. In addition to her work for PrepScholar, Hayley is the author of Museum Hack's Guide to History's Fiercest Females.

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