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Unread 26-10-2006, 20:13
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Re: When logic and calculus collide

Quote:
Originally Posted by KenWittlief
starting velocity is easy to straighten out. They dont both have to start at the same time. One person might be late for the race, and run up to the starting line and run across it, so his starting velocity was not zero.

But that means he could run faster for the whole race and just catch up at the finish line. They never ran at the same speed at any point.

thinking they both started at the same time is a mistaken assumption. In fact, according to the laws of physics it would be impossible for them both to start at exactly the same instant (point in time). (action and reaction - time for sound to reach the ear of both runners - human response time for sound to cause legs to move... the two runners could never start perfectly synchronised, one will always start before the other).
Ken, you've only shown that this theorem is only true for continuously differentiable functions of position. Your first argument is true if and only if the runner can go from 0 velocity to high velocity instantly, that is, without passing through any velocities in between, with infinite acceleration. That's physically impossible.

Starting time doesn't make a lick of difference. If one starts a second after the gun and runs at speed A, and the other starts 10 seconds late, he has to run at speed A+foo to get to the finish line at the same point. And you can't physically get from 0 to A+foo without going through A at some point.

Arguments about them not starting at the same time or place are beside the point. If you want to argue that the world's not perfect well fine. Toss all your fancy mathematics and physics in the trash because you can come up with some real world situations that are completely different from the stated problem.
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