  We investigate the power of the velocity drift ($\Delta v$) on cosmological
parameters and expansion history with observational Hubble data (OHD), type Ia
supernova (SNIa). We estimate the constraints of $\Delta v$ using the Fisher
information matrix based on the model by
\citet{pasquini2005codex,whitelock2006scientific}. We find that $\Delta v$ with
20 years can reduce the uncertainty of $\Omega_m$ by more than 42% than
available observations. Based on the statistical figures of merit (FoM), we
find that in order to match the constraint power of OHD and SNIa, we need 21
and 26 future measurements, respectively. We also quantitatively estimate for
the first time the number of years required for the velocity drift to become
comparable with current observations on the equation of state $w$. The
statistical FoM indicate that we need at least 12 years to cover current
observations. Physically, we could monitor 30 quasars for 30 years to obtain
the same accuracy of $w$. Considering two parameterized deceleration factor
$q(z)$, we find that the available observations give an estimation on current
value $-0.9 \lesssim q_0 \lesssim -0.3$. Difference between the two types of
$q(z)$ is the precise determination of variation rate $dq/dz$. For the first
model with constant $dq/dz$, $\Delta v$ with only 10 years provides a much
better constraint on it, especially when compared with SNIa. However, we need
$\Delta v$ for more years in the variable $dq/dz$ model. We find that $\Delta
v$ with 30 years reduces the uncertainty of transition redshift to
approximately three times better than those of OHD and SNIa.
