# How to Calculate Acceleration

In physics terms, acceleration, *a*, is the amount by which your velocity changes in a given amount of time. Given the initial and final velocities, *v** _{i}* and

*v*

*, and the initial and final times over which your speed changes,*

_{f}*t*

_{i}*and*

*t*

*, you can write the equation like this:*

_{f}In terms of units, the equation looks like this:

Distance per time squared? Don’t let that throw you. You end up with time squared in the denominator because you divide velocity by time. In other words, *acceleration* is the rate at which your velocity changes, because rates have time in the denominator. For acceleration, you see units of meters per second^{2}, centimeters per second^{2}, miles per second^{2}, feet per second^{2}, or even kilometers per hour^{2}.

It may be easier, for a given problem, to use units such as mph/s (miles per hour per second). This would be useful if the velocity in question had a magnitude of something like several miles per hour that changed typically over a number of seconds.

Say you become a drag racer in order to analyze your acceleration down the dragway. After a test race, you know the distance you went — 402 meters, or about 0.25 miles (the magnitude of your displacement) — and you know the time it took — 5.5 seconds. So what was your acceleration as you blasted down the track?

Well, you can relate displacement, acceleration, and time as follows:

and that’s what you want — you always work the algebra so that you end up relating all the quantities you know to the one quantity you *don’t* know. In this case, you have

(Keep in mind that in this case, your initial velocity is 0 — you’re not allowed to take a running start at the drag race!) You can rearrange this equation with a little algebra to solve for acceleration; just divide both sides by *t*^{2} and multiply by 2 to get

Great. Plugging in the numbers, you get the following:

Okay, the acceleration is approximately 27 meters per second^{2}. What’s that in more understandable terms? The acceleration due to gravity, *g**,* is 9.8 meters per second^{2}, so this is about 2.7 g’s — you’d feel yourself pushed back into your seat with a force about 2.7 times your own weight.