You probably recall Newton's second law of motion. Did you know that Newton actually wrote his second law in terms of momentum? In modern words, his law would read: the change in momentum of an object over a certain amount of time is equal to the total force applied to it. The change in momentum of an object divided by the time over which the change occurs is equal to the total force applied to it, and has the same direction as that of the applied force. Let's see how we can derive this equation from the familiar form of Newton's second law: "force equals mass times acceleration." Recall that acceleration is the rate of change of velocity in time, or D v over D t. So the force, F, is equal to mass times the rate of change of velocity divided by elapsed time. D v is the change in velocity, which is equivalent to the difference between the final and initial velocities. Thus our equation becomes force equals mass times the difference between the final velocity, v2, and the initial velocity, v1, divided by the elapsed time, D t. Expanding the equation gives us F equals m times v2 minus m times v1, divided by D t. But we know that mass times initial velocity v1 is the object's initial momentum, and mass times final velocity v2 is the final momentum. By rewriting the force equation in terms of the rate of change of momentum, we obtain Newton's original definition. In other words, the average force on a body equals the resulting change in momentum divided by the time elapsed in the process.

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