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 d2x
--- = ---
d t d t2
so the dimension has to be Mass (M)times Length(L) divided by (Time(t) squared)
ML
---
T2
or in SI units this becomes kg m s-2 | 
