  In this paper we will consider the dynamics of BPS and non-BPS Dp-branes in
the background of N Dk-branes. Our approach is based on an existence of the new
symmetry of D-brane effective actions that naturally emerges in the near
horizon region of the stack of N Dk-branes. Since generally this scaling
symmetry is explicitly broken in the Lagrangian we will find the equation that
determines the time evolution of the generator of this transformations. Then we
will argue that in case when the tachyon living on the worldvolume of unstable
D-brane reaches the stable minimum the time evolution of this generator can be
easily determined. With the help of the knowledge of the time dependence of
this charge we will determine the trajectory of the non-BPS D-brane in the near
horizon region of N Dk-branes. In case of BPS Dp-brane probe we will aruge that
such a broken scaling symmetry exists as well and the existence of the explicit
time dependence of the generator of this symmetry can be used in the solving
the equation of motion of the probe Dp-brane in the near horizon region of N
Dk-branes.
