  We study a tachyon cosmological model based on the dynamics of a 3-brane in
the bulk of the second Randall-Sundrum model extended to more general warp
functions. A well known prototype of such a generalization is the bulk with a
selfinteracting scalar field. As a consequence of a generalized bulk geometry
the cosmology on the observer brane is modified by the scale dependent
four-dimensional gravitational constant. In particular we study a power law
warp factor which generates an inverse power-law potential $V\propto
\varphi^{-n}$ of the tachyon field $\varphi$. We find a critical power $n_{\rm
cr}$ that divides two subclasses with distinct asymptotic behaviors: a dust
universe for $n>n_{\rm cr}$ and a quasi de Sitter universe for $0<n<n_{\rm
cr}$.
