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.
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