Final answer:
This question relates to physics principles such as conservation of momentum and kinetic energy applied to different collision scenarios between two objects with varying masses and velocities.
Step-by-step explanation:
The condition described involves two objects, A and B, moving toward each other, with object A having twice the mass of object B. The question appears to cover multiple scenarios of collisions between these two masses and how the principles of conservation of momentum and conservation of kinetic energy apply.
For example, in an elastic collision where object A, three times more massive than object B, is moving at a speed of 12 m/s towards object B which is also moving at 12 m/s but in the opposite direction, we can calculate the final velocities using conservation laws. Similarly, in a totally inelastic collision, where object B is at rest and twice as massive as object A moving at 24 m/s, we can determine the final speed of the combined mass after collision.
To establish if momentum is conserved in a collision where they move together post-collision, we can compare the total momentum before and after the collision. Conservation of momentum dictates that the momentum must be the same before and after the event if there are no external forces.
Lastly, in scenarios where two objects collide elastically or inelastically with equal or different masses and given initial velocities, we determine the final velocities of both objects after the collision while ensuring the results comply with the conservation principles.