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Why does kinetic energy increase as velocity squared?

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It’s certainly not intuitive (I know, science is often not intuitive, but still). Worse, you would think that momentum would go up hand in hand with kinetic energy, when the formulas above instead show the latter going up much faster due to the exponent. This also doesn’t make sense. read more

In an inelastic collision where there is no interaction (i.e. no potential energy), the energy is conserved and the only energy is the kinetic energy. So in inelastic collisions with no interactions, we find that the total of a quantity proportional to the velocity squared is conserved. read more

Say the amount of gas burned to increase speed by 10 m/s is 100 energy units, and the car's mass is 2. Then increasing from 10 to 20 with ke = 1/2 mv2 should increase the KE by 100. Therefore from 20 to 30 it should also be 100, resulting in 200 total energy units and 2x gas burned. read more

Since kinetic energy is a defined quantity it is meaningless to ask why it increases quadratically with velocity, it does because it is defined that way. The above argument gives a reason as to why it is defined that way. read more

The original question was: … the formula for kinetic energy is E=\frac{1}{2}mv^2 and the formula for momentum is P=mv . I ran into these in physics class long ago and was really bothered by the first formula. How can energy go up as the square of the velocity? read more

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The Scientific Worldview: Why is Velocity Squared?
thescientificworldview.blogspot.com

Why is velocity squared in kinetic energy?
physics.stackexchange.com