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Would I have to report following too closely then? It's apparently described as "careless" driving.
You can always contact admissions to ask. If it is a misdemeanor in your state, and you didn’t have it dismissed via deferred disposition or defensive driving or what have you, I, personally, would report it.
I can’t imagine that it’d hurt you at all. If anything, someone will read it, and, without hesitation, throw it back in the normal pile.