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Suvat vector versus the scalar form
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[QUOTE="kuruman, post: 6834336, member: 192687"] You argue correctly, of course. However, the equivalence is not at all reinforced by day to day usage in everyday life or in statements of physics problems. Even though there is equivalence, we say, "the pirate treasure is buried 4 m North of this tree"; we don't say, "the pirate treasure is buried - 4 m South of this tree." Likewise, in a physics problem, when we want to provide magnitude and direction, we say "the velocity of car A is 4 m/s towards car B"; we don't say "the velocity of car A is -4 m/s away from car B." Despite the equivalence, humans have an aversion for negative signs which introduces an asymmetry in usage to avoid the confusion that might arise from a double negative. My point is that this asymmetry leads one to think of a vector component of a vector, i.e. ##-A_y~\hat y## as a magnitude ##|A_y|## times a direction ##(-\hat y)##. Up to this point that's OK. But then comes the physics teacher who says that ##A_y##, the y-component of vector ##\vec A##, is a scalar. At this point one erroneously concludes "therefore scalars are "always" positive." When vectors are first introduced, I think that usage of the term "scalar" should be avoided even if accompanied by a relaxed definition, as [USER=493650]@PeroK[/USER] suggests in #29, because it invites trouble. A vector is usually introduced as a mathematical entity that has magnitude and direction. If then we define a scalar as an entity that has magnitude only but no direction, ##~\dots~## oops, I mentioned the M-word which is used for a positive quantity only. In my opinion, there is no good way to introduce scalars properly at the intro level. If I stop and think about it, I see no harm done by not mentioning scalars at that level either. [/QUOTE]
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Suvat vector versus the scalar form
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