  The parametrizations $q=q_0+q_1 z$ and $q=q_0+q_1 (1-a/a_0)$
(Chevallier-Polarski-Linder parametrization) of deceleration parameter, which
are linear in cosmic redshift $z$ and scale factor $a$, have been frequently
utilized in the literature to study kinematics of Universe. In this paper, we
follow a strategy that leads to these two well known parametrizations of
deceleration parameter as well as an additional new parametrization
$q=q_0+q_1(1-t/t_0)$, which is linear in cosmic time $t$. We study the features
of this linearly time-varying deceleration parameter in contrast with the other
two linear parametrizations. We investigate in detail the kinematics of the
Universe by confronting the three models with the latest observational data. We
further study the dynamics of the Universe by considering the linearly
time-varying deceleration parameter model in comparison with the standard
$\Lambda$CDM model. We also discuss future of the Universe in the context of
the models under consideration.
