The velocity selector is a classic first-year physics problem that demonstrates the influence of perpendicular electric and magnetic fields on a charged particle. Traditionally textbooks introduce this problem in the context of balanced forces, often asking for field strengths that would allow a charged particle, with a specific target velocity, to pass through the field region with constant velocity. While this analysis is quite useful from a pedagogical perspective, especially for checking to see if students remember their Newtonian mechanics from first semester, it is just one meaningful application of the velocity selector. In fact, a recent conversation with the author's physics class yielded an important question: What is the shape of a particle's path whose initial velocity does not match the target velocity? While the class was in agreement that the path would be "curved," they were at a loss for more detail. Solving this problem analytically can be difficult, especially for introductory physics students, given that the direction and magnitude of the magnetic force (and by extension, the particle's acceleration) change in time.