Physics with Calculus/Mechanics/Relative Motion

In an approximation termed Galilean relativity, when two objects are moving at ${\vec {u}}$ and ${\vec {v}}$ relative to a common inertial reference frame, the relative velocity between the two objects, in the frame of reference where one of them is still, is

${\vec {v}}_{\mathrm {ref} }={\vec {v}}-{\vec {u}}$