Why does kinetic energy increase quadratically, not linearly, with speed? (2011)

	Why does kinetic energy increase quadratically, not linearly, with speed? (2011)(physics.stackexchange.com)
	375 points by ProxyTracer 56 days ago \| 207 comments
	tl;dr: Two intuitive arguments derive KE ∝ v² without invoking work or mgh. The first uses a spring pushing two equal-mass boxes apart, combined with conservation of momentum and Galilean invariance of potential energy, to show KE(2v) = 4·KE(v). The second uses a free-falling object in a constant gravitational field, applying energy conservation in both directions (catching at quarter-heights vs. launching in quarter-energy increments) to squeeze KE(v) = 4·KE(v/2) from two opposing inequalities.
	HN Discussion: •Potential energy conversion provides the most intuitive explanation via height-to-speed comparison •Calculus-based derivation from F=dp/dt and E=F·dx is the clearest intuition ↑Symmetry-based arguments (Galilean invariance) are the deepest explanation, aligning with the article's approach •Constant force yields quadratic distance over time, so energy scales quadratically with velocity ↓The article doesn't truly answer the intuitive question of why going faster requires disproportionately more energy