If you are traveling at 60 mph, what is the total distance you will travel between perceiving a need to brake and coming to a complete stop?
A. 40 feet
B. 118 feet
C. 240 feet
Answer (2)
Convert the speed from mph to fps: 60 mph = 88 fps .
Calculate the reaction distance: 88 fps × 1.5 s = 132 feet .
Estimate the braking distance: 2 × 32.2 × 0.7 8 8 2 ≈ 171.78 feet .
Calculate the total stopping distance: 132 feet + 171.78 feet ≈ 303.78 feet . The closest answer from the options is 240 feet .
Explanation
Understanding the Problem We are given a scenario where a driver is traveling at 60 mph and needs to come to a complete stop. We need to determine the total distance traveled during this process, considering both the reaction time and the braking distance.
Defining Stopping Distance The total stopping distance is the sum of the reaction distance (the distance traveled during the driver's reaction time before applying the brakes) and the braking distance (the distance traveled while the brakes are applied until the vehicle stops).
Converting Speed to Feet per Second Let's assume a reaction time of 1.5 seconds. First, we need to convert the speed from miles per hour (mph) to feet per second (fps). We know that 1 mile = 5280 feet and 1 hour = 3600 seconds. Therefore: 60 mph = 60 × 3600 seconds 5280 feet = 88 fps
Calculating Reaction Distance Now, we can calculate the reaction distance: Reaction Distance = Speed × Reaction Time = 88 fps × 1.5 s = 132 feet
Estimating Braking Distance Next, we need to estimate the braking distance. A common approximation for braking distance is given by the formula: Braking Distance = 2 × g × friction v 2 where v is the speed in fps, g is the acceleration due to gravity (approximately 32.2 ft/s 2 ), and the friction coefficient for dry pavement is approximately 0.7. Plugging in the values: Braking Distance = 2 × 32.2 × 0.7 8 8 2 = 45.08 7744 ≈ 171.78 feet
Calculating Total Stopping Distance and Choosing the Answer Finally, we can calculate the total stopping distance: Total Stopping Distance = Reaction Distance + Braking Distance = 132 feet + 171.78 feet ≈ 303.78 feet Comparing this to the provided answer choices (40 feet, 118 feet, 240 feet), the closest reasonable answer is 240 feet. However, our calculated value is significantly higher, suggesting that the actual braking distance might be larger or the assumed friction coefficient might be lower. Given the options, 240 feet is the most plausible.
Final Answer Based on our calculations, the total stopping distance is approximately 303.78 feet. However, considering the provided options, the closest and most reasonable answer is 240 feet.
Examples
Understanding stopping distances is crucial for road safety. For instance, knowing the approximate stopping distance at different speeds helps in maintaining a safe following distance. If you're driving and see a potential hazard ahead, estimating your stopping distance can help you determine if you have enough space to brake safely, potentially preventing an accident. This concept is also vital in urban planning, influencing traffic signal timing and intersection designs to minimize the risk of collisions.
The total stopping distance when traveling at 60 mph is calculated to be approximately 303.78 feet, consisting of both the reaction distance and the braking distance. The closest option given in the multiple-choice answers is 240 feet . Thus, based on the calculations, the selected answer is 240 feet.
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