# Formula: Relativistic Velocity Addition Velocity in system S    Relative velocity    Velocity in system S'    Speed of light

## Velocity in system S

Unit
We consider two intertial systems S and S'. Here $$u$$ is the velocity of a body in the reference frame S at rest.

If, for example, two spaceships seen from the resting earth (system S'), each fly with 0.6-fold speed of light in opposite direction, then one spaceship (body) moves away with 0.88x speed of light from the view of the other spaceship (system S) and not, as one would expect classically with 1.2x speed of light: \begin{align} u &~=~ \frac{0.6\,c ~+~ 0.6\,c}{1 ~+~ \frac{ 0.6\,c ~\cdot~ 0.6\,c}{c^2}} \\\\ &~=~ \frac{1.2}{1 ~+~ 0.6 \cdot 0.6} \, c \\\\ &~=~ 0.88 \, c \end{align}

## Relative velocity

Unit
Relative velocity of the systems S and S'.

## Velocity in system S'

Unit
Velocity of a body in the reference frame S'.

## Speed of light

Unit
Speed of light is a physical constant and indicates how fast light travels in empty space (vacuum). It has the following exact value in vacuum: $$c ~=~ 299 \, 792 \, 458 \, \frac{ \mathrm{m} }{ \mathrm{s} }$$

## The Most Useful Physics Formula Collection on the Internet

+ Perfect for high school and undergraduate physics students
+ Contains over 500 illustrated formulas on just 140 pages
+ Contains tables with examples and measured constants
+ Easy for everyone because without vectors and integrals