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Q: Why does kinetic energy increase as velocity squared?
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”.
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