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. 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,
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
If an objects starts at rest, so that vi = 0, then
The distance an accelerating object moves is
If an object starts at rest, so that vi = 0, and we ask how far it travels, so xi = 0, then
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?