What Is the Work Energy Theorem?

The work-energy theorem is a generalized description of motion that states that the work done by the sum of all forces acting on an object is equal to the change in that object's kinetic energy. This principle of work and its relationship to kinetic energy is a core mechanical physics concept.

The work-energy theorem describes the direct relationship between work and energy. Its formula shows that net work done by forces acting on a particle causes a change in that particle's kinetic energy.

Work is an action that is performed on an object or system and that transfers energy from one location to another or from one form to another. The basic mathematical formula is work = force x distance.

Kinetic energy is the energy of motion that an object or system has at a given point in time. The basic mathematical formula is kinetic energy = 1/2 x mass x velocity².

Since work = energy, the formulas for each can be substituted to create the following work-energy equation: force x distance = 1/2 x mass x velocity². This equation often is transformed into a set of other equations called the “kinematic equations.”

The work-energy theorem can be derived from Newton's second law of motion, which concerns the inversely proportional relationship between acceleration and mass, and the directly proportional relationship between acceleration and net force.

Kinetic energy and work are measured in the same units.

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