We are often interested in how fast the velocity is changing. "How fast is something getting faster?" 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
Sometimes we may want to know about velocity and displacement and not be interested in the time. For those situations, we can play with these equations and come up with a third one --
v2 = vi2 + 2 a (x - xi)
With this equation, we might answer questions like, "Starting from rest and accelerating at 1.5 m/s2, how far has a car traveled when its speed is 100 km/hr?"
These are our Big Three Kinematics Equations that we will use many, many times. Become familiar and comfortable with them.
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) 2005, Doug Davis; all rights reserved