When logic and calculus collide

[Lil' Lavery]

Originally Posted by GRaduns340

It makes sense.

I'm not sure your assumption of the starting velocities being the same is completely true though. Technically, there is no derivative of the position graph at zero, because the derivative doesn't exist at the endpoints of a graph. Logically, yes, their velocities are both 0, but in order to use a derivative to prove it you would have to assume that the runners were both at rest before the start of the race, but with a lack of that knowledge there is no way to find f'(0).

You'd actually have to prove that it was an intermediate time at which their velocities were the same, like Tim suggested. I don't know if you've done it yet, but the mean value theorem would be useful there. (I think I pulled out the right name).

Yeah, we used the Mean Value Theorem to prove it via calculus. And according to calculus, their starting velocities don't have to be equal to 0, but I know calculus can prove it, I was wondering if it worked logically.
I suppose that the two speeds would have to be equal at some point, but I can't help this feeling that there's some way that it could be done with never having the same speed.