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Physics Face-off: The Momentum Principle vs. Newton's 2nd Law

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Consider the following physics problem. An object with a mass of 1 kg and a velocity of 1 m/s in the x-direction has a net force of 1 Newton pushing on it (also in the x-direction). What will the velocity of the object be after 1 second? (Yes, I am using simple numbers—because the numbers aren't the point.) Let's solve this simple problem two different ways. For the first method, I will use Newton's Second Law.
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