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_{f},
and the initial and final times over which your speed changes, t_{i} and t_{f},
you can write the equation like this:
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.
