A dynamic holographic optical trap uses a dynamic diffractive optical element such as a liquid crystal spatial light modulator to realize one or more optical traps with independent controls. Such holographic optical traps provide a number of flexibilities and conveniences useful in various applications. One key requirement for such a trap is the ability to move the trapped microscopic object from one point to the other with the optimal velocity. In this paper we develop a nematic liquid crystal spatial light modulator based holographic optical trap and experimentally investigate the optimal velocity feasible for trapped beads of different sizes, in such a trap. Our results show that the achievable velocity of the trapped bead is a function of size of the bead, step size, interval between two steps and power carried by the laser beam. We observe that the refresh rate of a nematic liquid crystal spatial light modulator is sufficient to achieve an optimal velocity approaching the theoretical limit in the respective holographic trap for beads with radius larger than the wavelength of light.