What is the equation for kinetic energy?

The correct equation for kinetic energy is given by the relationship KE = 0.5mv². This formula indicates that the kinetic energy (KE) of an object is directly proportional to its mass (m) and the square of its velocity (v). The factor of 0.5 arises from the derivation of the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

In context, as the velocity of an object increases, its kinetic energy increases exponentially since it is proportional to the square of the velocity. This means that if you were to double the velocity of an object, its kinetic energy would increase by a factor of four. This makes the kinetic energy equation a crucial component in understanding many concepts in physics, particularly in dynamics and motion.

The other choices represent different physical quantities and relationships. The equation involving mgh pertains to gravitational potential energy, while the equations involving mv and 2mv do not accurately represent the relationship between kinetic energy and velocity. This is fundamental to solving problems in mechanics and analyzing the energy dynamics of moving objects.