Final answer:
The second hand of a clock has a positive angular velocity moving clockwise, but when it decelerates and stops, the angular acceleration is negative. Therefore, answer B (ω is positive and a is negative) is the correct description of its motion as it slows down.
B is correct
Step-by-step explanation:
When observing the second hand of a clock on the wall coming to a halt, we need to understand its angular velocity (ω) and angular acceleration (a). Initially, since most clocks move in a clockwise direction, their angular velocity vector is typically into the wall, following the right-hand rule. When the second hand is moving, its angular velocity (ω) is positive since it's rotating clockwise, which is considered the negative direction by convention. As the clock's battery stops and the second hand decelerates, the change in angular velocity (Δω) over the change in time (Δt) defines the angular acceleration (a). Because the speed of the second hand is decreasing, the angular velocity is becoming less negative, which means a is negative.
Hence, as the second hand comes to a stop, the angular velocity is positive because it is moving clockwise, but slowing down. The angular acceleration is negative because the second hand is decelerating, decreasing its angular velocity. The correct answer is B. ω is positive and a is negative.