Time is not seen as a dimenson by everybody (not even by Einstein himself, if memory serves). This makes the “diversion”-idea quite troublesome (or awkward). Even the “diversion” thought itself doesn’t make things any transparent: Given space dimensions, a time “dimension” is necessarily something entirely different and cannot be compared 1 to 1.
I don’t think you need the concept of time dimension here nor the two dimensional car example here. The equation is simply saying “as I see your motion through space increase I see your motion through time decrease”. Decreasing motion through time is precisely the concept of time dilation.
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