  We use numerical simulations to examine the mass-velocity and
intensity-velocity relations in the CO J=2-1 and H$_2$ S(1)1-0 lines for
jet-driven molecular outflows. Contrary to previous expectations, we find that
the mass-velocity relation for the swept-up gas is a single power-law, with a
shallow slope $\simeq -1.5$ and no break to a steeper slope at high velocities.
An analytic bowshock model with no post-shock mixing is shown to reproduce this
behaviour very well.
  We show that molecular dissociation and the temperature dependence of the
line emissivity are both critical in defining the shape of the line profiles at
velocities above $\sim$ 20 km s$^{-1}$. In particular, the simulated CO J=2-1
intensity-velocity relation does show a break in slope, even though the
underlying mass distribution does not. These predicted CO profiles are found to
compare remarkably well with observations of molecular outflows, both in terms
of the slopes at low and high velocities and in terms of the range of break
velocities at which the change in slope occurs. Shallower slopes are predicted
at high velocity in higher excitation lines, such as H$_2$ S(1)1-0.
  This work indicates that, in jet-driven outflows, the CO J=2-1 intensity
profile reflects the slope of the underlying mass-velocity distribution only at
velocities $\le $ 20 km/s, and that higher temperature tracers are required to
probe the mass distribution at higher speed.
