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For example, let's say that in a linear physics problem, all the data are given to a certain direction, and coded positively for direction to the right.

So +5m/s would be a velocity of 5m/s to the right.

And lets say after some calculation you get a negative answer, implying the direction was therefore to the left. (-2m/s for example), would it be therefore incorrect to state -2m/s to the left? Would this not be like saying the opposite of 2m/s to the left, and therefore to the right?

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I wouldn't say it's necessarily incorrect, but it's certainly a bit confusing. If you have a coordinate system set up beforehand, you shouldn't need to reference "to the left" or "to the right" as well as specifying the components of the velocity. The information is all right there in the velocity components. It seems to just add confusion.

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This is not necessarily incorrect I think, but not very clear either. Because one cannot automatically assume that everyone thinks that positive is right and negative is left, one could instead say "in the direction of motion" or "opposite the direction of motion" to denote the direction in a clear and non-biased way.

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