So if T is independent, then the issue becomes is the 14 correct if the equation is to work for the generalized equation for a trek of many people or individuals or people sitting at home.
One question, how do you get to:
T = (-14 plusminus (196-4s)^.5)/2
That may be my problem, even though this started as a kind of fun spoof thing for me, I take seriously what you are saying because my food could depend on it or people's safety.
I think the issue is, mathematically, you cannot include enough processes, differentials, or variables in different levels of mathematical process to make a formula that will work in this example. Although the usefulness of them is that they will prevent disasters by predicting a range of values which will work.
Again, while I was spoofing at first, thus the reference to the made up unpublished treatise, you guys are right on ... I just don't think the "theorum" or "formula" or "equation" will work in realtity.
Thus, like Godels proof, even within a mathematical system let alone when it is applied to realtiy, the system cannot generate its own proof, or in the case of the general theorum of existence of unique solutions, this may be a kind of tautology. Input in = input out, or confirmation that given the intitial hypothesis there will only be one answer, regardless of the realities the formula is trying to measure. Does that make sense to you?
This is starting to interest me so much I can't stop thinking about it, but no harm meant on my side. I wrote a spoofy answer and got back what is expected at this site, a really great answer.
Update: T may not be independent, because of the length of time travelled each day, or the length of time it takes to travel x distance, or some other function of time, even though it is a constant as we measure it. Thus, c becomes important in your equation, because it may not be zeroed out because s(0)=0. So the question that really starts to loom, and I was afraid of this given my mind and interest in this, is: if c, in your equation cannot be established without empirical data, can it be cancelled out ... and can s(0)=0 for more than one set of facts????