Deriving vave = (vo + v)/2 (AP)

A Graphical Approach:

under construction

An Analytical Approach:

This innocent-looking equation requires some mathematical knowledge that you might not get until your second semester of calculus, since the average value of a continuous function is a calculus concept, but here goes:

Suppose that an object has a speed vo at time t = 0, and a speed v at time t = T. We know that v = vo + at if the object's acceleration is constant. The average value of the function y = f(x) between x = a and x = b is defined as ave val def, so the average velocity, vave is:

equations 1 and 2

Now, if v = vo + at, then at = v -vo, and:

equations 3 and 4

Which is what we set out to prove.

last update January 10, 2005 by JL Stanbrough