  We study the properties of a D-brane in the presence of $k$ NS5 branes. The
Dirac-Born-Infeld action describing the dynamics of this D-brane is very
similar to that of a non-BPS D-brane in ten dimensions. As the D-brane
approaches the fivebranes, its equation of state approaches that of a
pressureless fluid. In non-BPS D-brane case this is considered as an evidence
for the decay of the D-brane into ``tachyon matter''. We show that in our case
similar behavior is the consequence of the motion of the D-brane. In particular
in the rest frame of the moving D-brane the equation of state is that of a
usual D-brane, for which the pressure is equal to the energy density. We also
compute the total cross-section for the decay of the D-brane into closed string
modes and show that the emitted energy has a power like divergence for $D0$,
$D1$ and $D2$ branes, while converges for higher dimensional D-branes. We also
speculate on the possibility that the infalling D-brane describes a decaying
defect in six dimensional Little String Theory.
