  Teleparallel gravity is a modified theory of gravity for which the Ricci
scalar $R$ of the underlying geometry in the action is replaced by an arbitrary
functional form of torsion scalar $T$. In doing so, cosmology in $% f(T)$
gravity becomes greatly simplified owing to the fact that $T$ contains only the
first derivatives of the vierbeins. The article exploits this appealing nature
of $f(T)$ gravity and present cosmological scenarios from hybrid and
logarithmic teleparallel gravity models of the form $% f=e^{mT}T^n $ and
$f=D\log(bT)$ respectively, where $m$, $n$, $D$ and $b$ are free parameters
constrained to suffice the late time acceleration. We employ a well motivated
parametrization of the deceleration parameter having just one degree of freedom
constrained with a $\chi^{2}$ test from 57 data points of Hubble data set in
the redshift range $0.07<z<2.36$, to obtain the expressions of pressure,
density and EoS parameter for both the teleparallel gravity models and study
their temporal evolution. We find the deceleration parameter to experience a
signature flipping for the $\chi^{2}$ value of the free parameter at
$z_{tr}\simeq0.6$ which is consistent with latest Planck measurements. Next, we
present few geometric diagnostics of this parametrization to understand the
nature of dark energy and its deviation from the $\Lambda$CDM cosmology.
Finally, we study the energy conditions to check the consistency of the
parameter spaces for both the teleparallel gravity models. We find the SEC to
violate for both the models which is an essential recipe to obtain an
accelerating universe.
