The simplest situation we can imagine is when the particles have the
same final velocity ie that they ``stick together'' after the collision.
In that case momentum conservation is
sufficient to determine the final velocity because now there is a single
unknown final velocity, 
. Momentum conservation reads:
In fact the problem of any number of particles colliding has the same
type of solution.
Note that this type of collision in general entails conversion of some mechanical
energy into internal energy of the combined object. Denote this amount of
energy by 
then because total energy is conserved as is
linear momentum we can write
This type of collision is called a totally inelastic collision because
it is the type of collision in which the largest amount of mechanical
energy consistent with momentum conservation is converted to internal energy.