Acceleration describes the rate of change of velocity with respect to time.
Acceleration is a Vector Quantity, which means it has both a magnitude and a direction.
We typically denote acceleration by the letter a with an arrow over it. The arrow indicates that it is a vector quantity.
Average Acceleration
As you can see in Figure 1 below, the formula for acceleration over any time period is just the different between the initial and final velocities, divided by the time between the measurements.
Figure 1: Acceleration Formula for Average Acceleration
The above formula is for average acceleration over a period of time.
If we want to specifically note that we are talking about average acceleration, we use a bar over the a, like this:
This is shorthand for:
Instantaneous Acceleration
If we want to determine the instantaneous acceleration, all we have to do is take the same measurement, but at smaller and smaller intervals of time, until we get to a time (t) which is so infinitesimally small that it approaches zero. “Instantaneous” means happening in an “instant,” or practically no time at all. So if we make our first and second measurements as close together in time as theoretically possible, we have an instantaneous measure of acceleration.
This is what Figure 2, below, describes:
Related: Time, Rate of Change, Acceleration (Physics), Vectors, Vector Quantity, Velocity (Average), Velocity (Instantaneous), Angular Velocity