We investigate temporal cooperative behaviour in a realistic model of a molecular motor-cargo assembly by simulating a one-dimensional stochastic model of a motor-bound bead in an optical trap. Here, each motor is linked to a bead through an elastic spring, and performs forward and backward hopping motions on the filament. The rates characterising the forward and backward steps are different because of the free energy change associated with ATP hydrolysis. Apart from forward and backward hopping, motor bind to, and unbind from the filament with specific rates, while remaining attached to the bead. The bead is subjected to elastic force originating from the stretched motor-springs, thermal noise as well as an external force from an optical trap. We constructed a Gillespie code which can simulate the dynamics of up to six motors. Our results indicate that the emergence of cooperative behaviour, as observed in experiments, is closely connected with the load-sharing properties of the team. Simulation results of the mean first passage time show excellent agreement with experimental data of the same in the literature. © 2022, Indian Association for the Cultivation of Science.