Acceleration is the rate of change of the velocity. If Dv is the change in velocity in a time interval Dt, then the average acceleration over that time interval is


The instantaneous acceleration is defined as the average acceleration taken in the limit of very small time intervals:

Like velocity, acceleration is a vector quantity. Its is indicated by its algebraic sign.

The instantaneous acceleration can be found as the slope of the tangent to the curve on an v versus t graph at that particular time.

The average acceleration  from t=5 s to 7s is marked in the graph. Use the slider 1 (Dt) to reduce the time interval (Dt) to near zero and watch how the acceleration changes

Average Acceleration from tinitial:    to   tfinal:    is    equal to  

slider 1

slider 2

Compare this with the exact value of the  instantaneous acceleration found by taking the derivative. You can also use the slider 2 to find the instantaneous velocity at some other point.

Instantaneous acceleration at t= is