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Performance assessment is crucial during the motor design process as a basis for comparison between different candidate designs. The objective of this paper is to determine how quickly an air-core linear permanent-magnet synchronous motor can perform a point-to-point positioning task while not exceeding a given limit on allowable average power dissipation. The magnetic field in the air gap is obtained by solving the Poisson equation, and an explicit representation for the Lorentz force is derived. Using this force model, performance limits are identified by solving a family of optimal control problems numerically.