The most famous equation in physics is Einstein's equation E=mc^2 . In a very real sense this expresses the equivalence of mass and energy. Mass can be changed into energy and energy can be changed into mass. Mass can be thought of as a sort of 'frozen' energy.
According to the laws of Newtonian mechanics a constant force acting on a body of mass m produces a constant acceleration. A graph of speed against time will be a straight line, so according to Newtonian mechanics, after some time, the body being accelerated will be travelling faster than the speed of light, as shown below.
In practice, as soon as the speed reaches a significant fraction of the speed of light the acceleration starts to decrease. The inertial mass
of the object – the resistance of the object to further acceleration – increases, according to the equation
The increase in mass is a measure of the increase in energy of the body. The equation E=mc^2 only refers to the energy of a body at rest. The energy of a moving body is actually
The difference between this and
is the kinetic energy of the body.
Kinetic energy
For small
kinetic energy