  A particular class of space-time, with a tachyon field, \phi, and a
barotropic fluid constituting the matter content, is considered herein as a
model for gravitational collapse. For simplicity, the tachyon potential is
assumed to be of inverse square form i.e., V(\phi) \sim \phi^{-2}. Our purpose,
by making use of the specific kinematical features of the tachyon, which are
rather different from a standard scalar field, is to establish the several
types of asymptotic behavior that our matter content induces. Employing a
dynamical system analysis, complemented by a thorough numerical study, we find
classical solutions corresponding to a naked singularity or a black hole
formation. In particular, there is a subset where the fluid and tachyon
participate in an interesting tracking behaviour, depending sensitively on the
initial conditions for the energy densities of the tachyon field and barotropic
fluid. Two other classes of solutions are present, corresponding respectively,
to either a tachyon or a barotropic fluid regime. Which of these emerges as
dominant, will depend on the choice of the barotropic parameter, \gamma.
Furthermore, these collapsing scenarios both have as final state the formation
of a black hole.
