Re: When logic and calculus collide
 

I'm sorry to have misrepresented my skepticism on the subject. I was not trying to make any point or mute point. My only inquiry was about acceleration.
You did point out that the negative acceleration would be off the charts when running into a lamp post and it would be much higher than a normal runner would be used to. Also it could not be measured by means in a foot race.
My objection is that infinity could not be reached negatively or positively in the real world.
A bullet, for example, stops instantly to our eyes, but it starts instantaneously to our eyes as well, and your argument stated that the ramp up is true, but not the ramp down. Even if it could not be measured, wouldn't logic state it couldn't get to be an infinite instantaneous stop if the runner hits a lamp post and just a very negative slope?

Re: When logic and calculus collide
 

you are correct, in the normal sense of physics and math, even when you run into a brick wall you do not experience infinite acceleration to zero velocity. therefore as your velocity dropped to zero you would cross a point where your velocity would match the other runner (instantaniously).

I was only trying to show that when you try to apply pure mathematics to the physical world you almost always run into problems.

The math courses I took in college, when we were talking about things that I could correlate into physical realities, I could grasp them easily. Then when things became abstract and imaginary (6 dimensional space for example), I had a difficult time.

It was not until years after I graduated that I understood that most math we learn in college does not really apply to the real world (as I mentioned in a previous post).

To correct my example of an exception, an infinite force could stop a runner instantainously (infinite acceleration to zero velocity), in which case there would be a discontinuty in the velocity graph. Infinity is a valid number in math, but not in physics.

"Two runners start a race at the same time". Ok in math class, impossible in physics. The given statement is illogical in the real world. The question supposes an impossible situation, but they still want to know the 'correct' answer.

When Logic and Calculus Collide. The professors question itself is illogical.

Re: When logic and calculus collide
 

I absolutely agree and understand. Thank you.

Re: When logic and calculus collide
 

I don't know why I'm bumping this or was even reading this thread, but I can say that this is entirely possible. Just in higher dimensions. Nothing said they have to move in a straight path.