Final answer:
For a car traveling west and slowing down, the acceleration is opposite to its motion. Considering west as the negative direction, the correct answer is (a) Positive, because the deceleration implies a positive acceleration towards the opposite direction, i.e., east.
Step-by-step explanation:
The question concerns a car that is traveling west and slowing down, which involves analyzing the direction of its acceleration. Since acceleration is defined as the rate of change of velocity, if a car is slowing down, its acceleration is opposite in direction to its velocity. In this context, since west is considered the negative direction (-x direction), and the car is slowing down while moving west, the acceleration is directed east, which is the positive direction in our coordinate system.
Therefore, when the car is decelerating (slowing down) while moving in a negative direction, the acceleration is positive. This is akin to the car having a negative velocity (due to moving west) and its speed is decreasing over time (which results in a positive change in velocity). So, the correct statement about the car's acceleration as it slows down in the negative direction is that the acceleration is positive.
In summary, when a car is moving in a negative direction and slowing down, it experiences a positive acceleration because the acceleration is directed opposite to the car's direction of motion, which is the positive direction of the coordinate system. Therefore, we choose only one option and mention the correct option in the final answer: (a) Positive.