  We study the behavior in the remote past and future of solutions of an
equation of motion for charged particles proposed by F. Rohrlich, for the
special case in which the motion is in one spatial dimension.
  We show that if an external force is applied for a finite time, some
solutions exhibit the property of ``preacceleration'', meaning that the
particle accelerates before the force is applied, but that there do exist
solutions without preacceleration. However, most solutions without
preacceleration exhibit ``postacceleration'' into the infinite future (i.e.,
the particle accelerates after the force is removed). Some may consider such
behavior as sufficiently "unphysical" to rule out the equation.
  More encouragingly, we show that analogs of the unphysical ``runaway''
solutions of the Lorentz-Dirac equation do not occur for solutions of
Rohrlich's equation. We show that when the external force eventually vanishes,
the proper acceleration vanishes asymptotically in the future, and the
coordinate velocity becomes asymptotically constant.
