To derive the kinetic energy expression, we begin with the work-energy relationship. The work-energy principle states that work done on an object is equal to the change in its kinetic energy. Work done when a force acts on an object can be expressed as force times distance, causing the body to move some distance in the direction of the applied force.

By Newton’s second law, force is defined as the product of mass and acceleration. If a body has acceleration, there is a change in its velocity. If the body starts from rest and the acceleration is uniform, its final velocity is determined by the distance and the acceleration of the body.

Putting the definition of force and distance into the equation for work done, we arrive at the work done on the object being related to its mass and the square of its velocity. The work done to accelerate an object from rest to some velocity goes directly into its kinetic energy.

Therefore, kinetic energy is defined as the energy an object has due to its motion, dependent on its mass and the square of its velocity. Therein, the interrelation of both mass and speed shows how important those values are in establishing the energy belonging to moving objects.

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