In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions. Computational solutions are generally not capable of producing exact answers and can therefore never completely replace conventional mathematics, but exact answers are not always needed, and for that reason an alternate approach to the problem may be worth pursuing. Since the correct answer to a problem is not always available, computational methods can be used as a means of verifying the results of more traditional mathematical problem solving.