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SUMMARY

The forum discussion centers on a Kinematics problem involving vector differential equations. The user expresses confusion about the transition from the second to the third line in their solution and questions the integration limits from u² to v². Chet clarifies that the substitution v² = x is used, which resolves the user's misunderstanding regarding the variable x representing position as a function of time.

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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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They make the substitution v2 = x.

Chet
 
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.
 

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