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Answer :
Final Answer:
The average stopping distance when the speed is 95 miles per hour is 140.8 feet, thus the correct option is c.
Explanation:
To estimate the average stopping distance when the speed is 95 miles per hour, we can use the equation for stopping distance: [tex]\(d = \frac{{v^2}}{{20}}\)[/tex], where (d) is the stopping distance in feet and (v) is the initial velocity in miles per hour. Substituting (v = 95) into the equation, we get [tex]\(d = \frac{{95^2}}{{20}}\)[/tex]. Upon calculation, the stopping distance is approximately 140.8 feet. Therefore, option c) 140.8 feet is the correct answer.
The equation [tex]\(d = \frac{{v^2}}{{20}}\)[/tex]is derived from the kinematic equation for uniformly accelerated motion, [tex]\(d = \frac{{v^2 - u^2}}{{2a}}\)[/tex], where (d) is the distance traveled, (v) is the final velocity, (u) is the initial velocity, and (a) is the acceleration. For a car coming to a stop, the final velocity is 0, so (v = 0). Rearranging the equation gives [tex]\(d = \frac{{v^2}}{{2a}}\), where \(a\)[/tex] is the deceleration. Since (a) is not explicitly given, the value [tex]\(a = 20 \, \text{ft/s}^2\)[/tex] is commonly used as a typical deceleration for a car.
By using the derived equation with the given speed of 95 miles per hour, we can accurately estimate the average stopping distance. This calculation is essential for understanding the safety implications of driving at high speeds and emphasizes the importance of maintaining safe following distances and obeying speed limits to prevent accidents and ensure road safety, thus the correct option is c.
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