Velocity Problem : Let's look briefly at the velocity problem. Several calculus books will treat it as its own problem. . In this problem we are given a position function of an object, f(t), which gives the position of an object at time t. Then to calculate the instantaneous velocity of the object we just have to recall that the velocity is nothing more than the rate at which the position is changing.
In other terms, to estimate the instantaneous velocity first we would calculate the average velocity,
A.V . = change in position/ time traveled
= f (t ) - f ( a ) /t - a
and then take values of t closer & closer to t = a & use these values to estimate the instantaneous velocity.