An easy way to remember the dimensions of the newton is to recall that it is a unit of force.

Force is a mass times an acceleration.

F = M x a a = d v dso the dimension has to be Mass (M)times Length(L) divided by (Time(t) squared)^{2}x --- = --- d t d t^{2}

ML --- T^{2}

or in SI units this becomes kg m s^{-2}