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In this paper we have constructed a coordinate space (or geometric)Lagrangian for a point particle that satisfies the exact Doubly SpecialRelativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next wedemonstrate how a Non-Commutative phase space is needed to maintain Lorentzinvariance for the DSR dispersion relation. Lastly we address the veryimportant issue of velocity of this DSR particle. Exploiting the aboveNon-commutative phase space algebra in a Hamiltonian framework, we show thatthe speed of massless particles is $c$ and for massive particles the speedsaturates at $c$ when the particle energy reaches the maximum value $\kappa $,the Planck mass.Comment: Minor changes, version to appear in PR

Lagrangian for doubly special relativity particle and the role of noncommutativity