Objects that collide and stick
When two objects lock together in a crash, the momentum from before is shared across their combined mass afterwards.
A worked example
A 900 kg car at 16 m/s hitting a stationary 600 kg car and locking on gives 14 400 = 1 500v, so v = 9.6 m/s.
The mistake people actually make
Add the two masses before dividing; using only the moving car's mass gives back its original speed. Momentum is conserved here even though kinetic energy is not.