  The $f(R,T)$ theory of gravitation is an extended theory of gravitation in
which the gravitational action contains both the Ricci scalar $R$ and the trace
of energy momentum tensor $T$ and hence the cosmological models based on
$f(R,T)$ gravity are eligible to describing late time acceleration of present
universe. In this paper, we investigate an accelerating model of flat universe
with linearly varying deceleration parameter (LVDP). We apply the linearly time
varying law for deceleration parameters that generates a model of transitioning
universe from early decelerating phase to current accelerating phase. We carry
out the state-finder and Om(z) analysis, and obtain that LVDP model have
consistency with astrophysical observations. We also discuss profoundly the
violation of energy-momentum conservation law in $f(R,T)$ gravity and dynamical
behavior of the model.
