  We derive asymptote solution of a homogeneous and isotropic universe governed
by the quadratic form of the field equation of $f(T)$ gravity. We explain how
the higher order of the torsion can provide an origin for late accelerated
phase of the universe in the FRW. The solution makes the scalar torsion $T$ to
be a function of the cosmic time $t$. We show that for the equation of state
$p=\omega \rho$ with $\omega\neq -1$ the scale factor represent late phase of
universe. We perform the cosmological studies and show how the quadratic form
of $f(T)$ effect on the behavior of these studies.
