Understanding the Law of Conservation of Momentum in One-Dimensional Collisions Between Two Objects Using the Velocity Space Approach

The law of conservation of momentum is a fundamental law of nature. It states that the momentum of an isolated system is conserved. In high school or introductory-level physics courses, for simplicity, teachers and textbooks always use collisions in one dimension as the examples to introduce the concept of conservation of momentum. To solve simple problems involving one-dimensional collisions, all we need are basic algebraic manipulations. However, the relation between physical quantities, such as mass and the changes in velocity and kinetic energy, of the colliding objects is not obvious. For instance, if an object A collides with a stationary object B, what is the direction of A after the collision? Is it possible that the final velocity of A is zero in an inelastic collision? In this paper, we argue that the so-called velocity space approach can be highly effective for physics teachers in building a better understanding of the law of conservation of momentum.