  A cosmological scenario with two branes (A and B) moving in a 5-dimensional
bulk is considered. As in the case of ecpyrotic and born-again braneworld
models it is possible that the branes collide. The energy-momentum tensor is
taken to describe a perfect barotropic fluid on the A-brane and a
phenomenological time-dependent "cosmological constant" on the B-brane. The
A-brane is identified with our Universe and its cosmological evolution in the
approximation of a homogeneous and isotropic brane is analysed. The dynamics of
the radion (a scalar field on the brane) contains information about the proper
distance between the branes. It is demonstrated that the deSitter type
solutions are obtained for late time evolution of the braneworld and
accelerative behaviour is anticipated at the present time.
