Question

momentum equals = mass (velocity)

yet for problems I end up using this

P = m (delta v)

what allows us to simply put the delta infront of the v to find the momentum?

Answer 1

Actually, (mass)x(delta V) is the CHANGE in momentum, not the momentum itself. You should write instead

(delta p) = (mass)x(delta V)

You can write it this way because the mass does not change, in most situations. One exception would be a rocket engine with mass leaving through the exhaust.