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why kinetic energy is proportional to $v^2$ and not to $v^3$, for instance.

https://www.physicsforums.com/threads/quadratic-forms-and-kinetic-energy.826884/

I wish to find reference for this.

Now I find your thread with the same question and very similar answers:

https://www.physicsforums.com/threa...gy-is-proportional-to-velocity-squared.78484/

Someone suggested a book Landau-Lifshitz Mechanics, but I do not find this derivation in it.

The final explanation to why kinetic energy is proportional to velocity squared

My question is, from where this derivation is.