A description of the martensitic transformations between the alpha, beta, and omega phases of titanium that includes nucleation and growth requires an accurate classical potential. Optimization of the parameters of a modified embedded atom potential to a database of density-functional calculations yields an accurate and transferable potential as verified by comparison to experimental and density-functional data for phonons, surface and stacking fault energies, and energy barriers for homogeneous martensitic transformations. Molecular-dynamics simulations map out the pressure-temperature phase diagram of titanium. For this potential, the martensitic phase transformation between a and 8 appears at ambient pressure and 1200 K, between alpha and omega at ambient conditions, between beta and omega at 1200 K and pressures above 8 GPa, and the triple point occurs at 8 GPa and 1200 K. Molecular-dynamics explorations of the kinetics of the martensitic alpha-omega transformation show a fast-moving interface with low interfacial energy of 30 meV/angstrom(2). The potential is applied to the study of defects and phase transformations of Ti.