Why does kinetic energy increase quadratically, not linearly, with speed? (2011)
A Physics Stack Exchange discussion explains that kinetic energy increases with the square of speed (KE = ½mv²) rather than linearly because work required to accelerate an object depends on both force and distance, and at higher speeds, the distance over which force is applied increases, leading to a quadratic relationship.
Background
- The question comes from Physics Stack Exchange, a Q&A site where physicists and students discuss theory. It addresses a classic puzzle in introductory mechanics: why kinetic energy (½mv²) depends on the square of velocity rather than just velocity itself.
- The deeper answer involves the work-energy theorem: the work needed to accelerate an object from rest equals force × distance. Since a faster-moving object covers more distance while being pushed (even if force is constant), the accumulated work — and thus the energy gained — grows with v², not v.
- A historical note: before Einstein, kinetic energy was thought to be exactly ½mv². Relativity showed this is only a low-speed approximation; at speeds near light, energy grows toward infinity, reflecting the deeper geometry of spacetime.