Equations like E=mc^2 and stuff like how the force og gravity becomes 1/4 as strong when the distance between the objects dobles. Similarly with braking distance with cars, double the speed and the braking distance quadruples. These all seem to fit so well.
Have we made math to fit so nicely with physics? Am I thinking of all this wrong? Since I feel it like it would be to big of a coincidense that we can so easily use equations to predic physics. What is actually the reason for this?
In: Mathematics
The universe is logically consistent and math is made to model that consistency. More specifically, I think the answer to what you are asking is calculus.
If you are in a vehicle with constant speed, your position will increase at a constant rate. However, if you have a constant acceleration then your velocity will increase at a constant rate and your position must increase at an exponential rate.
The squared term in both e=mc2 and kinetic energy (re braking) exist because of this kind of relationship.
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