  We search for velocity changes (i.e., acceleration/deceleration) of narrow
absorption lines (NALs) that are intrinsic to the quasars, using spectra of 6
bright quasars that have been observed more than once with 8-10m class
telescopes. While variations in line strength and profile are frequently
reported (especially in broader absorption lines), definitive evidence for
velocity shifts has not been found with only a few exceptions. Direct velocity
shift measurements are valuable constraints on the acceleration mechanisms. In
this study, we determine velocity shifts by comparing the absorption profiles
of NALs at two epochs separated by more than 10 years in the observed frame,
using the cross-correlation function method and we estimate the uncertainties
using Monte Carlo simulations. We do not detect any significant shifts but we
obtain 3$\sigma$ upper limits on the acceleration of intrinsic NALs (compared
to intervening NALs in same quasars) of $\sim$0.7 km s$^{-1}$ yr$^{-1}$
($\sim$0.002 cm s$^{-2}$). We discuss possible scenarios for non-detection of
NAL acceleration/deceleration and examine resulting constraints on the physical
conditions in accretion disk wind.
