This work develops a methodology for attaining trajectory-tracking tasks in a prescribed time when applied to perturbed wheeled mobile robots (WMRs). Specifically, car-like robots are considered in this control methodology. The vehicle kinematic model is first converted into two simple systems. Then, a prescribed time controller with a hybrid structure is developed. The hybrid controller combines a time-varying-gain controller and a sliding mode scheme to attain the control objective. The time-varying controller allows the closed-loop system to converge to a desired region with user-defined properties. Then, the time-varying controller is switched to a sliding mode methodology that compensates for matched disturbances and allows for achieving the trajectory-tracking task. A formal theoretical analysis is included to demonstrate the validity of the proposed control scheme. Moreover, the performance of the new scheme is assessed experimentally using a scaled WMR. These results reflect the efficiency of the prescribed time control methodology.