The main unit used for momentum has always been: kg*m/s

I believe there is no real reason for the momentum short letter to be “p”. I have spent a considerable amount of time on researching this and found nothing. Many websites say that, yt was traditionally the letter used and they cannot find the origins of the letter.

Also many physicists use another unit for momentum: Since impulse equals (F*t) = (m*v), you can simplify it by using the first term. In the metric system, that would be Newton∙seconds, N∙s. Further Research: UNC site