  We study the accelerated expansion phase of the universe by using the
{\textit{kinematic approach}}. In particular, the deceleration parameter $q$ is
parametrized in a model-independent way. Considering a generalized
parametrization for $q$, we first obtain the jerk parameter $j$ (a
dimensionless third time derivative of the scale factor) and then confront it
with cosmic observations. We use the latest observational dataset of the Hubble
parameter $H(z)$ consisting of 41 data points in the redshift range of $0.07
\leq z \leq 2.36$, larger than the redshift range that covered by the Type Ia
supernova. We also acquire the current values of the deceleration parameter
$q_0$, jerk parameter $j_0$ and transition redshift $z_t$ (at which the
expansion of the universe switches from being decelerated to accelerated) with
$1\sigma$ errors ($68.3\%$ confidence level). As a result, it is demonstrate
that the universe is indeed undergoing an accelerated expansion phase following
the decelerated one. This is consistent with the present observations.
Moreover, we find the departure for the present model from the standard
$\Lambda$CDM model according to the evolution of $j$. Furthermore, the
evolution of the normalized Hubble parameter is shown for the present model and
it is compared with the dataset of $H(z)$.
