  We study the second central extension of the (1+1) Aristotle Lie.We find that
the first central extension admit four orbits on the dual of second central
extension of the (1+1) Aristotle Lie group.The generic orbit is characterised
by a Hooke's constant k and a yank y.If the physics of the orbit is studied
with respect the evolution in time,it represents an elementary system with
internal energy U in a posotion-momentum under the conjugation of a Hooke's
force and a damping one proportional to the velocity as in particle
mechanics.If the physics of the orbit is studied with respect the evolution in
space, it represents an elementary system with an internal momentum P under the
conjugation of a kind of Hooke's force and a damping one proportional to a
slowness, slowness usually used in time travel waves.
