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There are two possible results. However, they cannot move in the same direction after the collision.

Total initial momentum = p - p = 0

where p represent the momentum of each object.

From the principle of conservation of momentum;

Total initial momentum = Total final momentum

Thus, Total final momentum = 0

There are only two possibilities for this:

1. Kinetic energy is conserved. (the collision is perfectly elastic)

In this case, they would move away from each other with the same magnitude of initial momentum.

2. Kinetic energy is not conserved. (the collision is inelastic)

In this case, they would either remain at rest or they will move away from each other with a smaller magnitude of initial momentum each had.

Note that if both bodies had moved in the same direction, there would be a net momentum in this direction and momentum would not have been conserved. (Momentum is ALWAYS conserved provided there is no external force acting on the system)

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