Abstract: Finding optimal trajectories for non-accelerating, non-holonomic agents is a well-understood problem. However, in video games, robotics, and crowd simulations non-holonomic agents start and stop frequently. With the vision of improving crowd simulation, we find optimal paths for virtual agents accelerating from a standstill. These paths are designed for the “ideal”, initial stage of planning when obstacles are ignored. We analytically derive paths and arrival times using arbitrary acceleration angle thresholds. We use these paths and arrival times to find an agent's optimal ideal path. We then numerically calculate the decision surface that can be used by an application at run-time to quickly choose the optimal path. Finally, we use quantitative error analysis to validate the accuracy of our approach.