  The aim of the article is to find a transformation that links the local
affine velocity of a non-rigid body in the laboratory inertial reference frame
$ S $ with the centro-affine velocity of motion of this body in the
accompanying accelerated frame $ k $. This paper is based on the kinematics of
a continuous medium and the generalized Lorentz transformation. In this paper
we show the 3D transformation of velocity linking the reference system $ S $
and the reference system $ k $, which moves without rotation. Wherein the
motion of various points of the rigid system $ k $ is inhomogeneous. Using
these formulas, we obtain the desired direct and inverse transformation of the
local affine velocity. Important special cases of this transformation are
considered. They are the motion of particles in a uniform force field and the
precession of Thomas. As an example of using the transformation of affine
velocity in $ S $, accelerated rotation of the disk was considered and the
local angular velocity and the magnitude of the deformation of its points were
calculated. Wherein, the calculated stretching coefficient is consistent with
the known one, and the formula found for the angular velocity is more general
than the earlier result obtained for uniform rotation of the disk.
