  The properties of a one space-dimension, one particle dynamical system under
the influence of a purely dissipative force are investigated. Assuming this
force depends only on the velocity, it is demonstrated, in contrast to the case
of linear damping, that there exist dissipative forces for which the particle
\textquotedblleft stops" in a finite time. It is also shown, by an explicit
example, that other dissipative forces exist such that they produce dynamics in
which the particle achieves zero velocity only after an infinite distance has
been traveled. Possible applications of these results to more complex
situations are discussed.
