In this paper, we present an optimal open-loop slew trajectory algorithm developed at GSFC for the so-called "Yardstick design" of the James Webb Space Telescope (JWST). JWST is an orbiting infrared observatory featuring a lightweight, segmented primary mirror approximately 6 meters in diameter and a sunshield approximately the size of a tennis court. This large, flexible structure will have significant number of lightly damped, dominant flexible modes. With very stringent requirements on pointing accuracy and image quality, it is important that slewing be done within the required time constraint and with minimal induced vibration in order to maximize observing efficiency. With reaction wheels as control actuators, initial wheel speeds as well as individual wheel torque and momentum limits become dominant constraints in slew performance. These constraints must be taken into account when performing slews to ensure that unexpected reaction wheel saturation does not occur, since such saturation leads to control failure in accurately tracking commanded motion and produces high frequency torque components capable of exciting structural modes. A minimum-time constraint is also included and coupled with reaction wheel limit constraints in the optimization to minimize both the effect of the control torque on the flexible body motion and the maneuver time. The optimization is on slew command parameters, such as maximum slew velocity and acceleration, for a given redundant reaction wheel configuration and is based on the dynamic interaction between the spacecraft and reaction wheel motion. Analytical development of the slew algorithm to generate desired slew position, rate, and acceleration profiles to command a feedback/feed forward control system is described. High-fidelity simulation and experimental results are presented to show that the developed slew law achieves the objectives.