Final answer:
The best diagram to represent a car coasting to the right and slowing down is one with positive velocity (rightward arrow) and negative acceleration (leftward arrow) due to road friction, depicted in FIGURE 2.14 (b).
Step-by-step explanation:
To represent a car that is coasting to the right and slowing down, we should reference FIGURE 2.14 (b), which depicts a car with negative acceleration in our coordinate system. In this scenario, the velocity of the car is positive (to the right), but the acceleration is opposite to the direction of motion (to the left).
This is shown in a free-body diagram by drawing an arrow to the right for the velocity of the car and an arrow to the left for the negative acceleration, which is caused by friction. The friction force, which opposes the forward motion of the car, is the force responsible for the car slowing down if we are ignoring air resistance.
Therefore, the correct free-body diagram would show a large arrow to the right representing forward motion and a smaller arrow to the left representing deceleration due to the friction force of the road.