  In this paper, we have considered a quadratic variation of the deceleration
parameter ($q$) as a function of cosmic time ($t$) which describes a smooth
transition from the decelerating phase of the Universe to an accelerating one
and also show some distinctive feature from the standard model. The logical
move of this article is against the behavior of the future Universe,
\textit{i.e.} whether the Universe expands forever or ends with a Big Rip, and
we observe that the outcome of the considered parametrization comes in favor of
Big Rip future of the Universe. The whole set up of the parametrization and
solution is taken in $f(R,T)$ theory of gravity for a spatially flat
Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry. Furthermore, we have
considered the functional form of $f(R,T)$ function as $% f(R)+f(T)$, where a
quadratic correction of the geometric term $R$ is adopted as the function
$f(R)$, and a linear matter term $f(T)$. We have investigated some features of
the model by examining the behavior of physical parameters. Our primary goal
here is to discuss the physical dynamics of the model in $f(R,T)$ gravity. We
have found, the EoS parameter also has the same singularity as that of the
Hubble parameter \textit{i.e.} at the initial phase and at the Big Rip. The EoS
parameter is explored in some detail for our choice of $f(R,T)$ function
considered here. Different cases for $f(R,T)$ functional form for different
values of the coupling parameters are discussed, and the evolution of the
physical parameters is shown graphically.
