  We consider moving-brane-solutions in AdS type back ground. In the first
Randall-Sundrum configuration, there are two branes at fixed points of the
orbifold symmetry. We point out that if one brane is fixed and the other brane
is moving, the configuration is still a solution provided the moving brane has
a specific velocity determined by its tension and bulk cosmological constant.
In the absence of the $\bf Z_2$ symmetry, we can construct multi-brane
configurations by patching AdS-Schwarzshild solutions. In this case, we show
that the 4-dimensional effective cosmological constant on the brane world is
not well defined. We find a condition for a brane to be stationary. Using the
brane scattering, we suggest a scenario of inflation on the brane universe
during a finite time, i.e, a scenario of a graceful exit of inflation.
