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Kinematics -- Vector DE

Homework Statement


f516dt.jpg


The Attempt at a Solution


Here's their solution.

5wca2r.jpg


I'm stuck on (b). The first and second lines are fine. But how do they get from the second line to the third line? And then in the fourth line, why are they integrating from u^2 to v^2?

EDIT: Sorry for the image size.
 
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Chestermiller said:
They make the substitution v2 = x.

Chet

That's it?! I thought x denoted position (as a function of time)! Was losing my mind over this. Thanks.