# What is the physical significance of Rapidity in Relativistic kinematics?

Recently I have came across a new term called rapidity in relativistic kinematics. We are using it in relativistic kinematics due to its additivity whereas velocity is not a additive quantity in relativistic case. But I am wondering that, is it introduced only to make our calculation easier or it does has any physical significance?

As a mind picture, imagine a set of travellators, like those you find in airports to convey passengers to flight gates. Each travellator moves at some constant speed $\Delta v$ relative to its immediate neighbor. Thus travellator 1 moves at speed $\Delta v$ relative to the airport, travellator 2 moves at the same speed increment $\Delta v$ faster than travellator 1 and in the same direction, travellator 3 moves at the same speed increment $\Delta v$ faster than travellator 2 and in the same direction and so on.
Then the rapidity of the motion on any given travellator relative to the airport frame is proportional to the aisle number $N$ of the travellator you're riding on. It will have rapidity $\eta = N\,\Delta v$, where we use natural units wherein $c=1$.
Put it another way: stepping from one travellator to the next always imparts the same boost matrix $B$ to one's co-ordinates. So the boost matrix linking the $N^{th}$ travellator's co-ordinates to the airport's is $\exp(N\,\log B)$. You can make the rapidity more and more like a continuous variable by imagining the speed $\Delta v$ to be smaller and smaller and imagining more and more travellators.