Final answer:
Momentum is conserved in the collision because no external forces are acting on the system, but kinetic energy may not be conserved since it can be transformed into other forms of energy. The final velocity of Object B would determine whether kinetic energy is conserved, but since it is unknown, we cannot make that conclusion.
Step-by-step explanation:
Understanding Momentum and Kinetic Energy in Collisions
When two objects collide, we analyze what happens to momentum and kinetic energy. Momentum is always conserved in isolated systems where no external forces are acting. In the given scenario, where two objects of equal mass collide and there are no external forces, the momentum before the collision must equal the momentum after the collision. This tells us that if Object A is at rest after the collision and Object B moves away with some unknown velocity, B must be moving with a velocity that maintains the total momentum of the system.
Kinetic energy, on the other hand, might not be conserved in an inelastic collision. Because Object A stops moving after the collision, it loses all its kinetic energy. If Object B gains all the kinetic energy Object A had before the collision, we would expect it to move away at the same speed Object A initially had, which is 12 m/s. However, kinetic energy can be transformed into other forms of energy during the collision, such as heat or sound. Due to the information given, where Object A comes to rest and we do not know the final velocity of Object B, we cannot make a definitive statement about the conservation of kinetic energy without additional details.
Thus, the correct answer is that momentum is conserved, but we cannot say for certain whether kinetic energy is conserved.