What would happen if instead of $F=m*d^2x/dt^2$, we had $F=m*d^3x/dt^3$ or higher?
Intuitively, I have always seen a justification for $\sim 1/r^2$ forces as the "forces being divided equally over the area of a sphere of radius $r$".
But why $n=2$ in $F=m*d^nx/dt^n$ ?
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