  We consider open strings attached to a moving D$_p$-brane with motion along
itself, in the presence of the backgrounds $B_{\mu \nu}$-field and a U(1) gauge
field $A_{\alpha}$. The effects of the motion of the brane on the open string
propagator and on the open string variables are studied. We observe that some
free parameters appear in the open string variables and in the propagator of
it.
