  Recently, in Gong {\em et al} \cite{GWW07} and Wang and Santos \cite{WS07} it
was shown that the effective cosmological constant on each of the two orbifold
branes can be easily lowered to its current observational value, by using the
large extra dimensions in the framework of both M-Theory and string theory on
$S^{1}/Z_{2}$. In this paper, we study the current acceleration of the
universe, using the formulas developed in \cite{WS07}. We first construct
explicitly time-dependent solution to the 10-dimensional bulk of the
Neveu-Schwarz/Neveu-Schwarz sector, compactified on a 5-dimensional torus.
Then, we write down the generalized Friedmann equations on each of the two
dynamical branes, and fit the models to the 182 gold supernova Ia data and the
BAO parameter from SDSS, using both of our MINUIT and Monte-Carlo Markov Chain
(MCMC) codes. With the best fitting values of the parameters involved as
initial conditions, we integrate the generalized Friedmann equations
numerically and find the future evolution of the universe. We find that it
depends on the choice of the radion potentials $V_{4}^{(I)} (I = 1, 2)$ of the
branes. In particular, when choosing them to be the Goldberger-Wise potentials,
$V_{4}^{(I)} = \lambda_{4}^{(I)} (\psi^{2} - {v_{I}}^{2})^{2}$, we find that
the current acceleration of the universe driven by the effective cosmological
constant is only temporary. Due to the effects of the potentials, the universe
will be finally in its decelerating expansion phase again. We also study the
proper distance between the two branes, and find that it remains almost
constant during the whole future evolution of the universe in all the models
considered.
