We are often interested in how fast the velocity is changing. This is the acceleration.
Acceleration is a change of velocity divided by a change of time so it has units of (meters/second)/second. We will write this as m/s/s or m/s2 (there are no "square seconds"). As with the velocity, we can describe the average acceleration or we can describe the instantaneous acceleration, the acceleration right now, at this particular moment,
This, too, is a derivative,
As with the velocity, we will usually mean the instantaneous acceleration if we simply say "the acceleration". We will often restrict ourselves situations with a constant acceleration; in that case the average acceleration is the same as the instantaneous acceleration.
We can take the definition of acceleration, turn it around, and write
The distance an accelerating object moves is
Consider a car that starts at rest and accelerates at 2 m/s/s for 3 seconds.
At that time, t = 3 s, how fast is it going? and how far has it gone?
(c) 2002, Doug Davis; all rights reserved