In Newtonian physics, what is the formula for kinetic energy?

The formula for kinetic energy in Newtonian physics is derived from the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. The correct formula, 1/2 mv^2, indicates that kinetic energy is directly proportional to the mass (m) of the object and the square of its velocity (v).

This means that as the mass of an object increases, its kinetic energy increases linearly, but as its speed increases, the kinetic energy will increase with the square of that speed. For example, if the velocity doubles, the kinetic energy will increase by a factor of four. The 1/2 in the formula accounts for the integration of force applied over the distance moved, leading to the final energy expression.

The other options do not accurately represent kinetic energy. The formula m^2v suggests a relationship that does not align with the fundamental definition of kinetic energy. Meanwhile, mv^2 and 2mv both ignore the crucial factor of taking half of the mass times the square of the velocity, which is essential in deriving the correct expression for kinetic energy. Thus, the formulation of kinetic energy as 1/2 mv^2 accurately encapsulates the relationship between mass and velocity in