Which formula represents the calculation for kinetic energy?

The formula that represents the calculation for kinetic energy is indeed given by the equation ( KE = \frac{1}{2} mv^2 ). This equation shows how the kinetic energy (KE) of an object is dependent on two key factors: its mass (m) and its velocity (v).

In this formula, mass is multiplied by the square of the velocity, and then the result is divided by two. The squaring of the velocity indicates that kinetic energy increases significantly with speed; for example, if an object's speed doubles, its kinetic energy actually increases by a factor of four because of the square. The concept of kinetic energy is crucial in mechanics as it allows us to understand the energy an object possesses due to its motion.

The other formulas provided pertain to different types of energy or force-related calculations. For instance, ( KE = mgh ) is the formula for gravitational potential energy, which is dependent on an object's height in a gravitational field. ( KE = mv ) does not account for the effect of velocity on energy in the correct way, while ( KE = Fd ) is the work-energy principle relating to the work done by a force over a distance.

Understanding that kinetic energy specifically relates to mass