 Here we have an example of a one-dimensional inelastic collision. Now, let's assume that we have two objects, one object, which is initially not moving and an object object, which is initially moving towards the first object at a speed of one meter per second. Those two objects are colliding and if the collision is 100% inelastic, then at the end they will travel together. So the question is, what is the final common speed of those objects? Now to solve this, we're going to use that linear momentum is conserved. Therefore, the momentum final must be equal to the momentum initial. This is a vector equation, therefore we should specify a coordinate system. So let's assume that to the right as usual is plus x. So in x direction, this one will slip into that mass 1 plus mass 2 traveling together at some final velocity is equal to mass 1 times its velocity initial plus mass 2 times its velocity initial. Now if I plug in the numbers for the right side, I'm going to have 0 for my initial momentum of object 1. So I only have the momentum of object 2, so I have 1 kilogram times minus, because I'm going against my x-coordinate system 1 meter per second. And on the left side, I have my total mass, so 1 kilogram plus 2 kilogram is 2 kilogram times. Now according to my drawing, the v final is to the left, therefore I would have to choose minus v final here according to my coordinate system. So what do I get? I get minus 1 kilogram meters per second is equal to 2 kilograms times v final and negative. So I divide by the minus 2 kilograms and I get v final. The final speed is 1 kilogram meters per second divided by 2 kilograms. The minus cancels each other. The kilogram cancels each other, so I get 0.5 meters per second as my final speed. And if I was asked what is the final velocity, I would have to say 0.5 meters per second to the left.