Velocity

The velocity $$\mathbf u$$ of a body in spacetime is given by

$$\mathbf u = \dfrac{d\mathbf r}{d\tau} = \gamma c\,\mathbf e_0 + \gamma \dot x\,\mathbf e_1 + \gamma \dot y\,\mathbf e_2 + \gamma \dot z\,\mathbf e_3$$ ,

where $$\mathbf r$$ is the body's position and $$\tau$$ is proper time. The velocity $$\mathbf u$$ has units of length / time.

See Also

• Position
• Momentum