  We investigate the post-acceleration of the $^{10}$Be fragment in Coulomb
breakup reaction of the halo nucleus $^{11}$Be, assuming that the excitation of
the projectile is to states in the low energy continuum. The method used
retains all finite-range effects associated with the interactions between the
breakup fragments and can use realistic wave functions for the halo nuclei. We
apply the method to compute the average momenta of the $^{10}$Be fragment at
four different scattering angles following breakup of $^{11}$Be on a Au target
at 42 MeV/nucleon beam energy. Our results, which are in qualitative agreement
with recent precision experimental data, are consistent with the picture of no
post-acceleration effect. The implication is that the breakup takes place on a
time-scale long compared to the collision time.
