QuestionJuly 19, 2025

8) Stopping a vehicle with good brakes from 20 miles per hour under good conditions requires about: a) 63 feet including thinking distance b) 80 feet including thinking distance c) 128 feet including thinking distance d) 186 feet including thinking distance

8) Stopping a vehicle with good brakes from 20 miles per hour under good conditions requires about: a) 63 feet including thinking distance b) 80 feet including thinking distance c) 128 feet including thinking distance d) 186 feet including thinking distance
8) Stopping a vehicle with good brakes from 20 miles per hour under good conditions requires about: a) 63 feet including thinking distance b) 80 feet including thinking distance c) 128 feet including thinking distance d) 186 feet including thinking distance

Solution
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Answer

a) 63 feet including thinking distance Explanation 1. Convert Speed to Feet per Second 20 miles per hour is converted to feet per second using the formula: \text{Speed (fps)} = \text{Speed (mph)} \times \frac{5280}{3600} . Thus, 20 \times \frac{5280}{3600} = 29.33 feet per second. 2. Calculate Stopping Distance The stopping distance includes both thinking and braking distances. Assuming average reaction time of 1.5 seconds, the thinking distance is 29.33 \times 1.5 = 44 feet. 3. Calculate Braking Distance Using the formula for braking distance: d = \frac{v^2}{2g\mu}, where v = 29.33 fps, g = 32.2 ft/s² (acceleration due to gravity), and \mu = 0.7 (friction coefficient for good brakes), we find d = \frac{(29.33)^2}{2 \times 32.2 \times 0.7} = 19 feet. 4. Total Stopping Distance Add thinking and braking distances: 44 + 19 = 63 feet.

Explanation

1. Convert Speed to Feet per Second<br /> 20 miles per hour is converted to feet per second using the formula: $ \text{Speed (fps)} = \text{Speed (mph)} \times \frac{5280}{3600} $. Thus, $20 \times \frac{5280}{3600} = 29.33$ feet per second.<br /><br />2. Calculate Stopping Distance<br /> The stopping distance includes both thinking and braking distances. Assuming average reaction time of 1.5 seconds, the thinking distance is $29.33 \times 1.5 = 44$ feet.<br /><br />3. Calculate Braking Distance<br /> Using the formula for braking distance: $d = \frac{v^2}{2g\mu}$, where $v = 29.33$ fps, $g = 32.2$ ft/s² (acceleration due to gravity), and $\mu = 0.7$ (friction coefficient for good brakes), we find $d = \frac{(29.33)^2}{2 \times 32.2 \times 0.7} = 19$ feet.<br /><br />4. Total Stopping Distance<br /> Add thinking and braking distances: $44 + 19 = 63$ feet.
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