Why is the energy of motion proportional to the square of the velocity?
Abstract
Based on a geometric demonstration by Johann Bernoulli, we show that the principles underlying the workenergy theorem are more fundamental than those discussed in the standard derivations. By introducing the notion of a mechanical Bernoulli process—a systematic process for destroying velocity and measuring work—we derive the relationship between the amount of work and the square of the velocity solely from the superposition of motion and the law of inertia.
 Publication:

American Journal of Physics
 Pub Date:
 August 2005
 DOI:
 10.1119/1.1927550
 Bibcode:
 2005AmJPh..73..701P
 Keywords:

 01.40.d;
 Education