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Q: Why does kinetic energy increase as velocity squared?

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Buckets of profoundly smart folk argued and debated about whether velocity (momentum) or velocity squared (energy) was the conserved quantity. Acceleration times time is velocity, so it should more-or-less make sense that force times time is momentum: . If it bothers you that energy doesn’t scale proportional to velocity, keep in mind that we’ve got that covered: momentum. Answer Gravy: Energy or work is force times distance: E=FD. It is so much easier to talk about position, velocity, and acceleration (intro physics) when you can say “acceleration is the derivative of velocity and velocity is the derivative of position”.