Sticky objects:

Look at the figure which is as shown below. The two objects contain masses m₁ and m₂, and they are moving at the speed of v1 and v₂, correspondingly. The velocity vectors v₁ and v₂ are not particularly shown here, but they point in the directions shown by the arrows. At A in this example, the two objects are on a collision course. The momentum of object with mass m1 is equivalent to p₁ = m₁v₁; the momentum of the object with mass m₂ is equivalent to p₂ = m₂v₂.

At B, the objects contain just hit each other and stuck altogether. Subsequent to the collision, the composite object cruises all along at a new velocity v which is distinct from either of the initial velocities. The new momentum, call it p, is equivalent to the sum of the original momentums. Hence:

p = m₁v₁ + m₂v₂

The final velocity v can be determined by reminding that the final mass is m₁ + m₂. And, hence:

p = (m₁+ m₂) v

v = p/(m₁+m₂)

Figure: (a) Two sticky objects, both with constant but distinct velocities, approach each other. (b) The objects after the collision.