A discussion of linear collisions between two or three objects is presented. This presentation has proved to be very effective in a junior-level course in analytical mechanics. The theoretical discussion uses a geometrical approach that treats elastic and inelastic collisions from a unified point of view. This approach gives the student a physical "feeling" for the effect of imposing varying amounts of inelasticity on a two- or three-body collision. Momentum and energy constraints are used to delimit the region, in the space of final velocities, that contains all possible solutions. Experiments with a linear air track demonstrate how changing the interparticle forces produces widely differing final states og motion.