Final answer:
The 1/2 mv² formula is the correct low-speed approximation for kinetic energy, valid when the object's velocity is much less than the speed of light.
Step-by-step explanation:
The formula for kinetic energy is correctly given by KE = 1/2 mv², where m is the mass of the object and v is its velocity. This formula represents the kinetic energy of an object moving at speeds much less than the speed of light. For very high velocities, close to the speed of light, a relativistic form of the kinetic energy formula must be used. Therefore, the correct answer is that the formula 1/2 mv² is the low-speed approximation to the correct formula.
The low-speed kinetic energy formula, KE = 1/2 mv², assumes that the velocity of the object is not approaching the speed of light (c), which makes relativistic effects negligible. As the speed of an object increases and gets significant fractions of c, the relativistic kinetic energy formula, which takes into account the Lorentz factor, must be used. At low speeds, the classical kinetic energy formula is an excellent approximation.