Final answer:
The average stopping distance on dry, level pavement when driving 45 mph is 292.649 meters, which includes the reaction distance and the braking distance. The reaction distance is the distance the car travels during the driver's reaction time, and the braking distance is the distance required for the car to come to a complete stop. By calculating these distances and adding them together, we can determine the total stopping distance.
Step-by-step explanation:
The average stopping distance on dry, level pavement when driving 45 mph can be calculated by considering the reaction time and the braking distance. First, let's calculate the reaction distance, which is the distance the car travels during the reaction time. Assuming a reaction time of 0.500 seconds, we can use the formula:
Reaction distance = (initial velocity * reaction time)
Since the initial velocity is given as 45 mph, we need to convert it to m/s:
45 mph = 20.1168 m/s
So, the reaction distance is:
Reaction distance = (20.1168 m/s * 0.500 s) = 10.0584 m
Next, let's calculate the braking distance. The braking distance can be determined using the formula:
Braking distance = (final velocity^2 - initial velocity^2) / (2 * acceleration)
For dry pavement, the acceleration is 7.00 m/s^2. Substituting the values:
Braking distance = (0^2 - 20.1168^2) / (2 * -7.00 m/s^2)
The negative acceleration arises because the car is decelerating. Simplifying the equation gives:
Braking distance = 282.59 m
Therefore, the total average stopping distance on dry, level pavement when driving 45 mph is the sum of the reaction distance and braking distance:
Total stopping distance = Reaction distance + Braking distance
Total stopping distance = 10.0584 m + 282.59 m = 292.649 m