  The solution of the Liouville equation for the ensemble of free particles is
presented and the classical analog to the quantum accelerating Airy wave packet
is constructed and discussed. Considering the motion of various classical
packets -- with an infinite and restricted distribution of velocities of
particles -- and also the motion of their fronts, we demonstrate in the
simplest and most definite way why the packet can display a more sophisticated
behavior (even acceleration) as compared with a free individual particle that
moves at a fixed velocity. A comparison of this classical solution with the
quantum one in the Wigner representation of quantum mechanics which provides
the closest analogy is also presented.
