Momentum is a vector quantity that is the product of the mass and the velocity of an object or particle. The standard unit of momentum magnitude is the kilogram-meter per second (kg · m/s or kg · m · s -1 ). Alternatively, the gram-centimeter per second (g · cm/s or g · cm · s -1 ) can be used to express momentum magnitude. The direction of a momentum vector can be expressed in various ways, depending on the number of dimensions involved, and is the same as the direction of the velocity vector.
Momentum, like velocity, is relative. Consider a 1,000-kg car moving at 20 m/s with respect to the surface of a highway, traveling northward. If you are driving the car, the momentum of the car relative to your body is zero. If you stand by the side of the road, the momentum of the car relative to you is 20,000 kg · m/s northward.
If you are driving a 1,000-kg car at 15 m/s with respect to the road and are traveling northward, and a truck of mass 1,500 kg is moving 20 m/s with respect to the road and comes up behind you in the same direction, the truck's momentum relative to you is the product of its relative velocity (5 m/s northward) and its mass (1,500 kg), or 7,500 kg · m/s northward. Relative to the truck, the momentum of your car will be in the opposite direction, and will be smaller: 5 m/s x 1,000 kg = 5,000 kg · m/s southward. Thus, if a collision occurs, the danger is greater to the object that is less massive.
If the above mentioned truck passes you going the opposite way on the road, its momentum relative to you is 35 m/s x 1,500 kg southward, or 52,500 kg · m/s southward. Relative to it, your momentum is 35 m/s x 1,000 kg northward, or 35,000 kg · m/s northward. In that situation, as with the rear-end scenario, the peril is greater to the less massive vehicle in the event of a collision.
Momentum, like velocity, can be expressed either as an average over a period of time or as an instantaneous value at a single moment in time.