Work in general transfers energy from one place to another or one form to another, and the following is an explanation of the work-energy principle as it applies to particle dynamics. It should be noted that in more general systems, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device.

## The Work-Energy Theorem

The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle . This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.

The work *W* done by the resultant (net) force on a particle equals the change in the particle's kinetic energy *E _{k}*:

where *v _{i}* and

*v*are the speeds of the particle before and after the change and

_{f}*m*is the particle's mass.

## Derivation

For the sake of simplicity, we will consider the case in which the resultant force *F* is constant in both magnitude and direction and is parallel to the velocity of the particle.
The particle is moving with constant acceleration *a *along a straight line.
The relationship between the net force and the acceleration is given by the equation *F* = *ma* (Newton's second law), and the particle's displacement *d* can be expressed by the equation:

which follows from the following kinematic equation:

The work of the net force is calculated as the product of its magnitude and the particle's displacement. Substituting the above equations yields: