When two objects collide, the outcome of the collision depends on several factors, such as the masses of the objects, their velocities before the collision, and the type of collision (elastic or inelastic).
In an idealized scenario, where there is no external force acting on the system and the collision is perfectly elastic, it is possible for both objects to come to rest after the collision. In such a case, the kinetic energy of the system would be completely converted into other forms of energy, such as potential energy or deformation energy. However, this situation is relatively uncommon in real-world scenarios.
In most cases, when two objects collide, one object will typically gain some of the kinetic energy from the other object, resulting in a redistribution of energy between them. As a result, it is more common for both objects to continue moving after the collision, although their velocities may be different from their initial values.
However, it is also possible for only one object to come to rest after the collision, particularly if one object is much more massive than the other. In such cases, the more massive object can absorb most of the energy from the collision, causing it to come to rest while the other object continues to move with a lower velocity.
To summarize, while it is possible for both objects to be at rest after a collision under certain idealized conditions, in most real-world scenarios, at least one of the objects will continue to move after the collision, and only one object coming to rest is also possible, depending on the relative masses and velocities of the objects.