Achieving smooth and efficient slew movements on telescope mounts is crucial for minimizing structural stress, reaching maximum velocities, and ensuring efficient operation. Traditional slew trajectory generation methods often fall short in optimizing trajectories for time, resulting in unnecessarily long slew times that reduce telescope efficiency and potentially affect observation opportunities. Additionally, traditional methods often fail to converge smoothly to tracking velocities, leading to abrupt changes in motion that can compromise settling time. This paper presents a novel time-optimal jerk-limited trajectory generator algorithm for slew movements and its current implementation at the SOAR telescope as part of the Mount Control Upgrade Project. This algorithm effectively addresses these limitations by simultaneously optimizing for user-defined constraints on position, velocity, acceleration, and jerk while achieving minimum time. The algorithm produces a jerk-constrained trajectory that converges to a constant velocity reference specified by position, velocity, and time (PVT) commands, ensuring smooth and efficient convergence to tracking velocities while minimizing structural stress and settling time. The proposed algorithm is simple to implement and can be used to generate smooth slew trajectories in telescopes and actuators in general.