What is the formula for kinetic energy?

The formula for kinetic energy is given as ½ × m × (v)², where "m" represents mass in kilograms and "v" signifies the speed in meters per second. This particular equation illustrates that kinetic energy depends not only on the mass of an object but also on the square of its velocity. The factor of ½ arises from the derivation of this formula from the work-energy principle, which relates the work done on an object to its change in kinetic energy.

To elaborate, kinetic energy is a scalar quantity that measures the amount of work an object can do due to its motion. The squared term (v)² emphasizes that if an object's speed doubles, its kinetic energy increases by a factor of four, demonstrating a quadratic relationship between speed and kinetic energy. This relationship is crucial in fields such as physics and engineering, where understanding the energy transformations in moving objects is essential.

In contrast, the other options presented represent different physical concepts. For instance, mass times acceleration due to gravity pertains to weight rather than kinetic energy. The multiplication of force and distance correlates with work done, not kinetic energy. Lastly, the change in velocity divided by time refers to acceleration, which is unrelated to the calculation of kinetic energy. Thus, the