  We study dynamics of a D3-brane propagating in the vicinity of k coincident
NS5 branes. We show that when $g_s$ is small, there exists a regime in which
dynamics of the D-brane is governed by Dirac-Born-Infeld action while higher
order derivative in the expansion can not be neglected. This leads to a
restriction on how fast scalar field may roll. We analyze the motion of a
rolling scalar field in this regime, and extend the analysis to cosmological
systems obtained by coupling this type of field theory to four dimensinal
gravity. It also leads to some FRW cosmologies, some of which are related to
those obtained with tachyon matter.
