  In this paper, we have examined the recently proposed modified symmetric
teleparallel gravity, in which gravitational Lagrangian is given by an
arbitrary function of non-metricity scalar $Q$. We have considered a constant
jerk parameter to express the Hubble rate. Moreover, we have used 31 points of
OHD datasets and 1701 points of Pantheon+ datasets to constraint our model
parameters by means of the Markov Chain Monte Carlo analysis. The mean values
and the best fit obtained give a consistent Hubble rate and deceleration
parameter compared to the observation values. In order to study the current
accelerated expansion scenario of the Universe with the presence of the
cosmological fluid as a perfect fluid, we have considered two forms of
teleparallel gravity. We have studied the obtained field equations with the
proposed forms of $f(Q)$ models, specifically, linear $f\left( Q\right) =\alpha
Q+\beta $ and non-linear $f\left( Q\right) =Q+mQ^{n}$ models. Next, we have
discussed the physical behavior of cosmological parameters such as energy
density, pressure, EoS parameter, and deceleration parameter for both model. To
ensure the validity of our proposed cosmological models, we have checked all
energy conditions. The properties of these parameters confirm that our models
describe the current acceleration of the expansion of the Universe. This result
is also corroborated by the energy conditions criteria. the Finally, the EoS
parameter for both models indicates that the cosmological fluid behaves like a
quintessence dark energy model.
