We study the accelerated expansion phase of the universe by using the 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≤z≤2.36\documentclass[12pt]{minimal}
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\begin{document}$$0.07 \le z \le 2.36$$\end{document}, larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter q0\documentclass[12pt]{minimal}
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\begin{document}$$q_0$$\end{document}, jerk parameter j0\documentclass[12pt]{minimal}
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\begin{document}$$j_0$$\end{document} and transition redshift zt\documentclass[12pt]{minimal}
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\begin{document}$$z_t$$\end{document} (at which the expansion of the universe switches from being decelerated to accelerated) with 1σ\documentclass[12pt]{minimal}
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\begin{document}$$1\sigma $$\end{document} errors (68.3%\documentclass[12pt]{minimal}
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\begin{document}$$68.3\%$$\end{document} 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 Λ\documentclass[12pt]{minimal}
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\begin{document}$$\Lambda $$\end{document}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).
