# Definite Integral

1. Jul 8, 2004

### quarky

(1) A ball is dropped from rest, and after t seconds its velocity is v ft/sec. Neglecting air resistance, show that the average velocity during the first T/2 seconds is 1/3 of the average velocity during the next T/2 seconds.
Will I integrate v? If so, what it is a function of?

2. Jul 8, 2004

### tomkeus

$$v(t)=gt$$
$$<v_1>=\frac{1}{\frac{T}{2}}\int_0^{\frac{T}{2}}gtdt$$
$$<v_2>=\frac{1}{\frac{T}{2}}\int_{\frac{T}{2}}^Tgtdt$$
$$T=\frac{v}{g}$$
You can figure out the rest I think.

Last edited: Jul 8, 2004
3. Jul 8, 2004

### e(ho0n3

v is a function of time. Do you remember how to obtain the average of a function over an interval?

4. Jul 22, 2004

### Phymath

A = 1/(b-a) S f(x) dx, where S is the intergral from a to b as ur limits