When logic and calculus collide

[KenWittlief]

Originally Posted by Kaizer007

I'm sorry this is four days late, but I wanted to ask how the last part of Ken's argument way up there makes sense:

which part of the runners body would you measure to use as their 'speed' when they hit a brick wall? What system would you use to measure the speed from the instant that, lets say, the skin on their forehead first contacts the wall, and the point when their head comes to a compete stop?

Radar? GPS? a high speed camera? If the impact has a 1µS duration I dont think it can be measured by any means associated with running a foot race. For all practical purposes the acceleration is off the scale (infinite), compared to what a runner normally experiences.

It seems to be a mute point anyway. As others have pointed out, the two runners started 'at the same time', even though the laws of physics say this is impossible

and everyone appears to be assuming the two runners run exactly the same distance, even though this is also impossible.

The 'math class' answer is that they must run at the same speed at some point, including the starting velocity of zero. (because they are really two points moving along straight lines).

The physics (and logical) answer is that they dont have to run the same speed at any instant to end up in a tie.

In fact, as far as I know, there is no rule against a runner approaching the finish line, looping around and going back to the starting line, and looping back to the finish line, to run 3 times the distance as the other runner. This means he could run 18 mph for the entire duration of the race, while the other runner runs at 6mph for the whole race, and they both cross the finish line at the same instant.

This is why I am an engineer and not a mathematician. When you think outside the box on a math test you get an F !