  Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to
the whole of the phase space, and assuming that this algebra is to be covariant
under action of deformed Lorentz generators, we derive the transformation
properties of positions under the action of deformed boosts. It turns out that
these transformations leave invariant the quadratic form in the position space,
which is the Minkowski metric and that the boosts saturate. The issues of
massless and massive particles motion, as well as time dilatation and length
contraction in this new framework are also studied.
