  The statistics of velocities in the cellular automaton model of Nagel and
Schreckenberg for traffic are studied. From numerical simulations, we obtain
the probability distribution function (PDF) for vehicle velocities and the
velocity-velocity (vv) correlation function. We identify the probability to
find a standing vehicle as a potential order parameter that signals nicely the
transition between free congested flow for sufficiently large number of
velocity states. Our results for the vv correlation function resemble features
of a second order phase transition. We develop a 3-body approximation that
allows us to relate the PDFs for velocities and headways. Using this relation,
an approximation to the velocity PDF is obtained from the headway PDF observed
in simulations. We find a remarkable agreement between this approximation and
the velocity PDF obtained from simulations.
