Final answer:
The outcome of a collision between two carts with equal mass depends on the type of collision. In an inelastic collision where the carts stick together, momentum is conserved, and the center-of-mass velocity remains constant, with the combined cart moving at a velocity less than the initial speed of the moving cart.
Step-by-step explanation:
When two carts with equal mass collide, several outcomes are possible, but the specific outcome depends on the nature of the collision, which can be elastic or inelastic. In the case of an inelastic collision, if the two carts stick together after the collision, as described in the provided scenarios, the carts would move with a common velocity after the collision because momentum is conserved. Based on the information given, if Cart A is moving and Cart B is initially at rest, after an inelastic collision where the carts stick together, the velocity of the center of mass of the system before and after the collision remains the same, albeit the carts would move at a velocity that is less than the initial velocity of Cart A.
For a graph of center-of-mass velocity versus time, it would remain constant both before and after the collision, assuming no external forces. The graph of momentum versus time for the system would also be constant because the total momentum of the system is conserved in the absence of external forces.