Suppose you have an isolated system in which two objects about to collide have equal and opposite momenta. if the collision is totally inelastic, what can you say about the motion after the collision?

Referring to the laws of conservation of momentum we have that there is a conservation of the linear impulse but there is a loss of kinetic energy on the system, this while the collision is inelastic.

From the theory we know that the momentum is preserved, therefore the initial momentum must be the same final momentum.

Both have equal vector magnitudes of their momentum but their directions are completely opposite, which would indicate that the initial and final momentum is zero. This while considering the aforementioned law.

For inelastic collisions there is the possibility that the objects will join after the collision, therefore the speed of the two objects is the same.

Therefore, the two objects are at rest after the collision.