The equation Ek = 1/2mv^2 defines kinetic energy, where the '1/2' is crucial for accurately representing the relationship between mass, velocity, and energy. This factor arises during the derivation from the work-energy principle, specifically when calculating work done on an object. Without the '1/2', the equation would incorrectly suggest that kinetic energy increases linearly with velocity rather than quadratically. The inclusion of '1/2' ensures that kinetic energy reflects the correct physical behavior of moving objects. Therefore, Ek cannot be simplified to mv^2 without losing essential accuracy in its representation.
