The transportation of the cargoes in biological cells is primarily driven by the motor proteins on filamentous protein tracks. The stochastic nature of the motion of motor protein often leads to its spontaneous detachment from the track. We formulate a mathematical model to study the effect of the detachment of motor protein on its track bound transport. We calculate two quantities: the distance traveled by the motor protein in given time, and the average time taken by a single motor protein to reach a target distance. Expectedly, both of these quantities decrease with the increasing detachment rate if the motor velocity is kept fixed. However, the existing experimental data suggest that a change in the detachment rate also affects the velocity of the motor protein. This relation between motor protein speed and its detachment rate results in a non-monotonic dependence on the distance traveled in fixed time and transport rate to a fixed distance. Therefore, we demonstrate that optimal motor speeds can be identified for the time and distance controlled conditions. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.