Why the velocity is negative
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Observe that the object below moves in the negativedirection with a changing velocity. An object which moves in the negative direction has a negative velocity. If the object is speeding up then its acceleration vector is directed in the same direction as its motion (in this case, a negative acceleration).
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Negative velocity just means velocity in the opposite direction than what would be positive. The velocity is a 3-dimension vector, there is no such thing as a positive or negative 3D vector.
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