Solving Definite Integral Problem: Average Velocity of Ball Dropped from Rest

[quarky]

Please help me! I got stuck on this problem:
(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?

 

[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.

 

[e(ho0n3]

Will I integrate v? If so, what it is a function of?

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

 

[Phymath]

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