A $\xi$-coloring of a graph $G$ is a coloring of the nodes of $G$ with $\xi$ colors in such a way any two neighboring nodes have different colors. We prove that there exists a $O(\Delta \log n)$ time distributed algorithm computing a $O(\Delta)$-colroing for unit disc graphs under the signal-to-interference-plus-noise ratio (SINR)-based physical model ($\Delta$ is the maximum degree of the graph). We also show that, for a well defined constant $d$, a $d$-hop $O(\Delta)$-coloring allows us to schedule an interference free MAC protocol under the physical SINR constraints. For instance this allows us to prove that any point-to-point message passing algorithm with running time $\tau$ can be simulated in the SINR model in $O(\Delta (\log n + \tau))$ time using messages of well chosen size. All our algorithms are proved to be correct with high probability.