In all isolated systems, total momentum is conserved:
ptot=ptot′.
Example
Car A (2.5 kg) begins at 1.5 m/s [fwd], while Car B (1.5 kg) beings at rest. Car A collides into Car B, and they stick together. What is the velocity of AB after the collision?
We begin with the conservation of momentum,
ptot=ptot′,
into which we substitute the individual momenta:
pA+pB=pAB′.
Now we can substitute the masses and velocities with
mAvA+mBvB=mABvAB′,
and solve for the final velocity:
vAB′=mABmAvA+mBvB.
Substituting the known values where [fwd] is positive, we have