Consider a ball thrown straight up and suppose it is caught by thrower after exactly 2 seconds.

h = height in feet of the ball

h = 0 is the heigth of throwing hand

t = time in seconds

In general, we learn from physics that

h(t) = a + bt - 16 t²

h(0) = h(2) = 0 implies a = 0 and b = 32

hence

h(t) = 32t - 16 t²

We calculate the average velocity during different time intervals:

Average velocity during the first second ==16 ft / s

Average velocity during the first 1 / 10 ^th second =

approaches 32 ft / s as n increases to infinity.

Thus the instantaneous velocity at t = 0 is 32 ft / s.