  We study the problem of a Herbig-Haro jet with a uniformly accelerating
ejection velocity, travelling into a uniform environment. For the ejection
density we consider two cases: a time-independent density, and a
time-independent mass loss rate. For these two cases, we obtain analytic
solutions for the motion of the jet head using a ram-pressure balance and a
center of mass equation of motion. We also compute axisymmetric numerical
simulations of the same flow, and compare the time-dependent positions of the
leading working surface shocks with the predictions of the two analytic models.
We find that if the jet is over-dense and over-pressured (with respect to the
environment) during its evolution, a good agreement is obtained with the
analytic models, with the flow initially following the center of mass analytic
solution, and (for the constant ejection density case) at later times
approaching the ram-pressure balance solution.
