kinetic energy

kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.

Kinetic energy for single objects is completely frame-dependent (relative). For example, a bullet racing by a non-moving observer has kinetic energy in the reference frame of this observer, but the same bullet has zero kinetic energy in the reference frame which moves with the bullet. The kinetic energy of systems of objects, however, may sometimes not be completely removable by simple choice of reference frame. When this is the case, a residual minimum kinetic energy remains in the system as seen by all observers, and this kinetic energy (if present) contributes to the system's invariant mass, which is seen as the same value in all reference frames, and by all observers.