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
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.