Here we have an example of one dimensional inelastic collision. Now let's assume that we have two objects, one object which is initially not moving and an object which is initially moving towards the first object at the speed of one meters 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? To solve this we're going to use that linear momentum is conserved. Therefore at the momentum final must be equal to the momentum initial. This is a vector equation therefore we should specify our coordinate system. So let's assume that to the right as usual is plus x. So in x direction this one will to slate 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. I've had plug in the numbers for the right side and going to have zero 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. 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 the final the final speed is 1 kilogram meters per second divided by 2 kilograms the minus cancel each other. The kilogram cancel 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.