momentum and velocity help?

Question

If I have negative velocity and I want to solve momentum question do I have to write negative sign of velocity in momentum formula or not like
V1M1+V1M2=V2M1+V2M2

Answer 1

for negative velocity the magnitude of the speed becomes negative, so the sign changes from positive to negative.

Answer 2

Let's say mass m moves to the left with speed v, and mass M moves to the right with speed V, and they collide head on.

Since momentum is a vector quantity and velocity is a vector quantity, the direction matters. Let things moving to the right have positive velocity, hence thnigs moving to the left have negative velocity.

So the initial momentum, Pi is

Pi = MV + m(-v) = MV -mv

The final momentum can be written as

Pf = MVf + mvf . Once you get the numberical values for any 5 of the 6 qauntities, the signs will sort themselves out. By this I mean if you are given M, m, V, v, and say Vf then teh sign on vf will be determined by the algebra you do to get the numerical value.