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In fact, let me go back to this equation here.
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You'll put time t=0, x doesn't have this term,
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doesn't have this term, and it is c.
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So I realize that the constant, c,
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is the initial location of the object,
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and it's very common to denote that by x0.
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So the meaning of the constant is
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where was the object at the initial time.
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It could've been anywhere.
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Simply knowing the acceleration
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is not enough to tell you where it was at the initial time.
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You get to pick where it was at the initial time.