Velocity vector and velocity intensity

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1. Dec 7, 2016

doktorwho

1. The problem statement, all variables and given/known data
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 $[0, \pi/2w]$
2. Relevant equations
3. The attempt at a solution

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 dont get correct results, where is my mistake?

2. Dec 7, 2016

haruspex

Which resulted in ....?
right.

3. Dec 8, 2016

doktorwho

Well.. isnt average acceleration then just $(v_i+v_f)/2$? Shouldnt i just get $aw$ then?

4. Dec 8, 2016

haruspex

Yes. No need to divide by the period.