Final answer:
The stopping distance of a car depends on factors including speed, road conditions, and driver reaction time. The stopping distance at 40 mph (d40) compared to the stopping distance at 15 mph (d15) would be longer due to a greater reaction distance and braking distance.
Step-by-step explanation:
The stopping distance of a car depends on various factors such as the speed of the car, road conditions, and the reaction time of the driver. In this case, we are comparing the stopping distance at 40 mph (d40) to the stopping distance at 15 mph (d15).
To calculate the stopping distance, we need to consider both the distance covered during the driver's reaction time and the distance covered while braking. The formula for the total stopping distance (TSD) is:
TSD = Reaction distance + Braking distance
The reaction distance is the distance the car travels during the driver's reaction time, and the braking distance is the distance covered while the car is decelerating. The braking distance depends on the speed of the car and the coefficient of friction between the tires and the road.
Let's assume a typical reaction time of 1 second. The reaction distance at 15 mph can be calculated as:
Reaction distance at 15 mph = (15 mph) × (1 hour/3600 seconds)
The braking distance depends on the speed of the car. According to Figure 2.34, for a car initially traveling at 30 m/s (67 mph), the braking distance is approximately 50 meters on dry pavement. Therefore, we can estimate the braking distance at 15 mph to be less than 50 meters.
Now, let's consider the stopping distance at 40 mph. The reaction distance at 40 mph is greater than the reaction distance at 15 mph because the car is traveling faster. Therefore, the total stopping distance at 40 mph (d40) is longer than the total stopping distance at 15 mph (d15).