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Safe trajectory planning for high-performance automated vehicles in an environment with both static and moving obstacles is a challenging problem. Part of the challenge is developing a formulation that can be solved in real-time while including the following set of specifications: minimum time-to-goal, a dynamic vehicle model, minimum control effort, both static and moving obstacle avoidance, simultaneous optimization of speed and steering, and a short execution horizon. This paper presents a nonlinear model predictive control-based trajectory planning formulation, tailored for a large, high-speed unmanned ground vehicle, that includes the above set of specifications. This paper also evaluates NLOptControl's ability to solve this formulation in real-time in conjunction with the KNITRO nonlinear programming problem solver; NLOptControl is our open-source, direct-collocation based, optimal control problem solver. This formulation is tested with various sets of the specifications. In particular, a parametric study relating execution horizon and obstacle speed, indicates that the moving obstacle avoidance specification is not needed for safety when the planner has a small execution horizon ($\leq0.375\;s$) and the obstacles are moving slowly ($\leq2.11\frac{m}{s}$). However, a moving obstacle avoidance specification is needed when the obstacles are moving faster, and this specification improves the overall safety by a factor of $6.73$ ($p=2.2\times10^{-16}$) without, in most cases, increasing the solve-times. Overall, the results indicate that (1) safe trajectory planners for high-performance automated vehicles should include the entire set of specifications mentioned above, unless a static or low-speed environment permits a less comprehensive planner; and (2) NLOptControl can solve the formulation in real-time.