We explore further the physical implications of Non-inertial Relativity. The spatial-force formalism of Non-inertial Relativity versus the proper-force description is analyzed. It is shown that contrary to what one would expect from the algebraic equation of an elliptic-hyperboloid, due to the constraint $ r = f v $ between the power $ r = { d E/d t }$ and the spatial force $ f = { d p/d t} $, the null-cone condition in phase space leads to the following bounds on the values of $ v $ and the Newtonian force $ f_N = m { d v/ dt} $ given by : $ 0 leq | v | leq c $, and $ 0 leq | f_N | leq b $. The fact that $ | f_N | leq b $ is bounded requires clear modifications to the Newtonian potential cite{Carlos-Newton}. We proceed to explore the group contractions of the pseudo-unitary group $ U(1,1)$ in the $ b ightarrow infty$ limit. After working with $dimensionless$ phase space coordinates one finds that it $does$ lead to Lorentz boosts transformations, in the $ b ightarrow infty$ limit, as expected. If, instead, one works with $dimensionful$ coordinates, the limit $ b ightarrow infty$ does $not$ lead to the standard Lorentz boosts transformations for the energy-momentum variables. There are extra terms that are associated with the semi-direct product of the Lorentz group with an Abelian group (which is not the Poincare group). Similar results were found by cite{Low}. We review the equivalence principle within the context of non-Milgromian modified Newtonian dynamics. An analysis is provided of how Non-inertial relativity points towards a space-time-matter unification. Finally, we conclude with some remarks about future avenues of research.