  In this paper we have constructed a coordinate space (or geometric)
Lagrangian for a point particle that satisfies the exact Doubly Special
Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we
demonstrate how a Non-Commutative phase space is needed to maintain Lorentz
invariance for the DSR dispersion relation. Lastly we address the very
important issue of velocity of this DSR particle. Exploiting the above
Non-commutative phase space algebra in a Hamiltonian framework, we show that
the speed of massless particles is $c$ and for massive particles the speed
saturates at $c$ when the particle energy reaches the maximum value $\kappa $,
the Planck mass.
