A mathematical model is developed which permits calculation of velocity changes of vehicles involved in a collision where one or both vehicles are articulated. This includes any single vehicle pulling a trailer (such as an automobile towing a recreational vehicle) or tractor, semitrailers. The equations of the model are based upon direct application of Newton's laws of impulse and momentum. Typically made assumptions (such as the insignificance of external impulses) are discussed and analyzed. Examples of the model's application are provided including the impact of tractor, semitrailers into rigid barriers.