Final answer:
Cart A's velocity would be positive (+2 m/s) while cart B's velocity would be negative (-1 m/s).
Step-by-step explanation:
In this scenario, cart A and cart B are moving in opposite directions. Assuming that the motion detector measures motion in the positive direction, cart A's velocity would be positive while cart B's velocity would be negative. This is because cart A is moving away from the motion detector, so its velocity is positive (+2 m/s). On the other hand, cart B is moving toward the motion detector, so its velocity is negative (-1 m/s).