Final answer:
Momentum is conserved in all types of collisions if no external forces act on the system. Kinetic energy conservation depends on whether the collision is elastic or inelastic. In the provided scenarios, momentum is conserved, but kinetic energy may not be.
Step-by-step explanation:
Is momentum conserved in all types of collisions? The answer is yes, momentum is conserved in all types of collisions, assuming there are no external forces acting on the system. However, kinetic energy may not always be conserved. In perfectly elastic collisions, both momentum and kinetic energy are conserved, whereas in inelastic collisions, only momentum is conserved, and kinetic energy is lost or transformed into other forms of energy.
In the scenario given, where two objects of equal mass collide and object A comes to rest while object B moves with some unknown velocity, since there are no external forces, we can say that momentum is conserved during the collision. The correct statement about this collision is that momentum is conserved, but kinetic energy is not necessarily conserved, as it depends on the nature of the collision—elastic or inelastic.
Even in the case where two objects of equal masses and velocities collide with each other and come to a rest, momentum is conserved because the total momentum before and after collision remains zero, which satisfies the law of conservation of momentum.