A frame moves with constant velocity along the axis of an inertial frame of Minkowski space. A particle moves with constant velocity along the axis of . Find the velocity of in .
The rapidity of any velocity is defined by . Find a relation between the rapidities of and .
Suppose now that is initially at rest in and is subsequently given successive velocity increments of (each delivered in the instantaneous rest frame of the particle). Show that the resulting velocity of in is
[You may use without proof the addition formulae and .]