  In the braneworld scenario ordinary standard model matter and
on-gravitational fields are confined by some trapping mechanism to the
4-dimensional universe constituting the D3-branes which are embedded in a (4 +
n)-dimensional manifold referred to as the bulk (n being the number of extra
dimensions). The notion of particle confinement is necessary for theories with
non-compact extra dimensions, otherwise, the particles would escape from our
4-dimensional world along unseen directions. In this paper, we have considered
a five-dimensional warped product space-time having an exponential warping
function which depends both on time as well as on the extra coordinates and a
non-compact fifth dimension. Further, we have assumed that the lapse function
may either be a constant or a function of both time and of the extra
coordinates, and have studied the nature of the geodesics of test particles and
analyzed the conditions of stability in this geometrical framework. We have
also discussed the possible cosmology of the corresponding (3 + 1)-dimensional
hypersurfaces.
