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sumolessons

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Somewhat related, but when I was sleep deprived and falling asleep during a general relativity lecture in college, I caught myself reasoning through the series of equations written by the professor on the board, and agreeing as to their validity with the explanation in my mind being that my parents are in a foreign country. My brain was convinced it had logically checked the progression and that it made sense, but it was based on this irrelevant fact. The experience always makes me wonder what falsehoods we individually or collectively use to convince ourselves of things being true.

Assuming the Newtonian framework F=dp/dt, p=mv, dW=Fdx, as well as constant mass, then Fdx=dpdx/dt=mvdv and integrating both sides gives deltaW=1/2mvf^2-1/2mvi^2+constant. So the amount of work to move the object from x1 to x2 is proportional to the difference of the square of the initial to final velocity squared up to a constant. This we define to be the change in kinetic energy.

But as others have mentioned this is only as intuitive as F=ma, or p=mv.

In my view, at least classically it's just a matter of definitions then. If our definitions of energy differ, the only thing we will experimentally agree on is the equation of motion, and even then up to a frame transformation.