# Relativistic Addition of Velocities

## Table of Contents

Consider two references frames. The second reference frame is moving at a velocity \( \small v \) relative to the first frame. The speed of an object is measured as \( \small u’ \) in the second reference frame. The speed of that same object as measured in the first reference frame, \( \small u \), is given by the relativistic velocity addition formula:

$$ u = \frac{v + u’}{1 + \frac{v \cdot u’}{c^2}} $$

Where

- \( \small u \) is the speed of the object as measured in the first reference frame,
- \( \small v \) is the speed of the second reference frame relative to the first reference frame,
- \( \small u’ \) is the speed of the object as measured in the second reference frame, and
- \( \small c \) is the speed of light in a vacuum.