Question

Acceleration: Suppose that a car traveling to the west (-x direction) begins to slow down as it approaches a traffic light. Which statement concerning its acceleration must be correct?

1) The car's acceleration is positive.
2) The car's acceleration is negative.
3) The car's acceleration is zero.
4) The car's acceleration cannot be determined without additional information.

Answer 1

The car's acceleration is positive because it is slowing down while moving in the negative direction, indicating the acceleration is toward the opposite, positive direction.

Step-by-step explanation:

When a car traveling to the west (which is the negative direction in our coordinate system) begins to slow down as it approaches a traffic light, it is experiencing deceleration. Deceleration means the car is undergoing an acceleration in the opposite direction of its velocity. Since the car is moving in the negative direction, for it to slow down, the acceleration must be in the positive direction (to the right, or eastward).

In this scenario, the correct statement concerning the car’s acceleration is that the car's acceleration is positive. This is due to the convention that in our coordinate system, the positive direction is to the right. Even though the car is moving to the left (negative direction), because it is slowing down, its acceleration is directed towards the right, thus it is positive. This involves a positive change in velocity (from a more negative value towards a less negative or higher value).