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and here's another context in which it's important.
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Suppose there is a mass m1,
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going with some velocity v1,
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and here's the second mass m2,
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going with some velocity v2; they collide.
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When they collide, all kinds of things can happen.
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I mean, m1 may bump its head on that and come backwards,
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or it could be a heavy object
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that pushes everything in the forward direction,
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or at the end of the day
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you will have some m1 going with a new velocity v1',
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and m2 going with a new velocity v2'.