Velocity vector and velocity intensity

[doktorwho]

Homework Statement

Given the velocity vector in the polar coordinates, ##\vec v=-awsin{wt}\vec e_r + awcos{wt}\vec e_\theta## determine the average velocity vector and velocity intensity over a time period ##[0, \pi/2w]##

Homework Equations

3. The Attempt at a Solution [/B]
For the first part where the average velocity vector is to be found i use
##\vec v_{avg}=\frac{\int_{0}^{\pi/2w}\vec vdt}{\pi/2w}##
and for the intensity part i use
##v=\sqrt{v^2_r+v^2_\theta}## first find the intensity which is just ##v=aw## and since the intensity is equal at all times i get for the second part
##\frac{2aw}{\pi/2w}## but i don't get correct results, where is my mistake?

 

[haruspex]

For the first part where the average velocity vector is to be found i use
##\vec v_{avg}=\frac{\int_{0}^{\pi/2w}\vec vdt}{\pi/2w}##

Which resulted in ...?

and for the intensity part i use
##v=\sqrt{v^2_r+v^2_\theta}## first find the intensity which is just ##v=aw## and since the intensity is equal at all times

right.

i get for the second part
##\frac{2aw}{\pi/2w}##

Think again about that step.

 

[doktorwho]

Which resulted in ...?

right.

Think again about that step.

Well.. isn't average acceleration then just ##(v_i+v_f)/2##? Shouldnt i just get ##aw## then?

 

[haruspex]

Well.. isn't average acceleration then just ##(v_i+v_f)/2##? Shouldnt i just get ##aw## then?

Yes. No need to divide by the period.