A kinetic study of growth of the superconducting phase in melt-quenched Bi₂Sr₂CaCu₂O_x has been performed by coloured optical microscopy. The pellets of Bi₂Sr₂CaCu₂O_x with the critical temperature at zero resistance (T_c,zero) of 66.8 K were melted and quenched by pouring on a steel plate. Upon annealing, the plate-like structure of the superconducting phase (2212) grew and showed a distinct colour in the polarized light of an optical microscope. The volume fraction of 2212 phase, as determined from the coloured optical micrographs, was analysed with the help of the Avrami transformation relation. The thickness of 2212 plates, measured by a scanning electron microscope, followed a power law of time with the exponent ranging between 3 and 5, and had an activation energy of 80 kJ mol^-1. The superconducting properties of the melt-processed samples were better than those sintered; the highest T_c,zero and transport critical current density (J_c) obtained were 85.3 K and 54.2 A cm^-2 at 77 K, compared with 66.8 K and 15.1 A cm^-2 at 55 K respectively for the sintered material. The optimum annealing temperature was found to be 820 degrees C. Annealing at temperatures higher than 820 degrees C decreased both T_c and J_c of melt-quenched Bi₂Sr₂CaCu₂O_x.