Kinetic energy (KE) is definitively proportional to the square of velocity (v^2) due to the principles of conservation of energy and the work-energy theorem. When a constant force (F) is applied to an object, the work done (A = F * dS) results in a change in kinetic energy that is mathematically derived from integrating the force over distance. This leads to the conclusion that the energy required to accelerate an object increases with the square of its velocity, as demonstrated through the equations of motion and calculus. The discussion clarifies that while energy input may appear constant, the rate of kinetic energy gain is not linear with velocity change.
PREREQUISITESPhysics students, educators, and anyone interested in understanding the fundamental principles of mechanics and energy dynamics in motion.