What is the average speed of a freely falling body starting from rest?

[camboguy]

Homework Statement

if a freely falling body starts from rest, then its displacement is given by s = (1/2) g(t^2). let the velocity after a time T be vsubt. Show that if we compute the average of the velocities with respect to t we get vsubave = (1/2)vsubt, but if we compute the average of the velocities with respect to s we get vsubave = (2/3)vsubt

The Attempt at a Solution

1)okay the first thing that i did was i found the derivate of s = (1/2)gt^2 to find the vsubt which i got vsuvt = gt.

2) next i vsubt that i found into the average value formula (1/(b-a))integralfora-to-b f(x)dx

3) then i got (g/(b-a))integralfora-to-b(t)

4)

 

[HallsofIvy]

You don't need to use an integral. At t= 0, s= 0 and at t, s= (1/2)gt^2 so the total distance moved is (1/2)gt^2. Divide that by t to get the average speed.