  We analyze the consistency of the ADM approach to KK model; we prove that KK
reduction commute with ADM splitting. This leads to a well defined Hamiltonian;
we provide the outcome. The electromagnetic constraint is derived from a
geometrical one and this result enforces the physical meaning of KK model.
Moreover we study the role of the extra scalar field we have in our model;
classical hints from geodesic motion and cosmological solutions suggest that
the scalar field can be an alternative time variable in the relational point of
view.
