#
Deriving v_{ave} = (v_{o} +
v)/2 (AP)

## A Graphical Approach:

## 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 v_{o} at time t = 0,
and a speed v at time t = T. We know that v = v_{o} + 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 ,
so the average velocity, v_{ave} is:

Now, if v = v_{o} + at, then at = v -v_{o},
and:

Which is what we set out to prove.

last update January 10, 2005 by JL
Stanbrough