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Stopping Distance The police department must determine the speed limit on a bridge such that the flow rate of cars is maximum per unit time. The greater the speed limit, the farther apart the cars must be in order to keep a safe stopping distance. Experimental data on the stopping distances d (in meters) for various speeds v (in kilometers per hour) are shown in the table. 20 40 60 80 100 d 5.1 13.7 27.2 44.2 66.4 (a) Convert the speeds v in the table to speeds s in meters per second. Use the regression capabilities of a graphing utility to find a model of the form d(s) = as² + bs + c for the data. (b) Consider two consecutive vehicles of average length 5.5 meters, traveling at a safe speed on the bridge. Let T be the difference between the times (in seconds) when the front bumpers of the vehicles pass a given point on the bridge. Verify that this difference in times is given by d(s) , 5.5 T + (c) Use a graphing utility to graph the function T and estimate the speed s that minimizes the time between vehicles.

Stopping Distance The police department must determine the speed limit on a bridge such that the flow rate of cars is maximum per unit time. The greater the speed limit, the farther apart the cars must be in order to keep a safe stopping distance. Experimental data on the stopping distances d (in meters) for various speeds v (in kilometers per hour) are shown in the table. 20 40 60 80 100 d 5.1 13.7 27.2 44.2 66.4 (a) Convert the speeds v in the table to speeds s in meters per second. Use the regression capabilities of a graphing utility to find a model of the form d(s) = as² + bs + c for the data. (b) Consider two consecutive vehicles of average length 5.5 meters, traveling at a safe speed on the bridge. Let T be the difference between the times (in seconds) when the front bumpers of the vehicles pass a given point on the bridge. Verify that this difference in times is given by d(s) , 5.5 T + (c) Use a graphing utility to graph the function T and estimate the speed s that minimizes the time between vehicles.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 31E
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Find the speed limit in the bridge such that the flow rate of vehicles is maximum per unit time.

Stopping Distance The police department must determine the speed limit on a bridge such that the flow rate of cars is maximum per unit time. The greater the speed limit, the farther apart the cars must be in order to keep a safe stopping distance. Experimental data on the stopping distances d (in meters) for various speeds v (in kilometers per hour) are shown in the table. v 20 40 60 80 100 d 5.1 13.7 27.2 44.2 66.4 (a) Convert the speeds v in the table to speeds s in meters per second. Use the regression capabilities of a graphing utility to find a model of the form d(s) = as² + bs + c for the data. (b) Consider two consecutive vehicles of average length 5.5 meters, traveling at a safe speed on the bridge. Let Tbe the difference between the times (in seconds) when the front bumpers of the vehicles pass a given point on the bridge. Verify that this difference in times is given by d(s) 5.5 T = + (c) Use a graphing utility to graph the function T and estimate the speed s that minimizes the time between vehicles. (d) Use calculus to determine the speed that minimizes T. What is the minimum value of T? Convert the required speed to kilometers per hour. (e) Find the optimal distance between vehicles for the posted speed limit determined in part (d).
Transcribed Image Text:Stopping Distance The police department must determine the speed limit on a bridge such that the flow rate of cars is maximum per unit time. The greater the speed limit, the farther apart the cars must be in order to keep a safe stopping distance. Experimental data on the stopping distances d (in meters) for various speeds v (in kilometers per hour) are shown in the table. v 20 40 60 80 100 d 5.1 13.7 27.2 44.2 66.4 (a) Convert the speeds v in the table to speeds s in meters per second. Use the regression capabilities of a graphing utility to find a model of the form d(s) = as² + bs + c for the data. (b) Consider two consecutive vehicles of average length 5.5 meters, traveling at a safe speed on the bridge. Let Tbe the difference between the times (in seconds) when the front bumpers of the vehicles pass a given point on the bridge. Verify that this difference in times is given by d(s) 5.5 T = + (c) Use a graphing utility to graph the function T and estimate the speed s that minimizes the time between vehicles. (d) Use calculus to determine the speed that minimizes T. What is the minimum value of T? Convert the required speed to kilometers per hour. (e) Find the optimal distance between vehicles for the posted speed limit determined in part (d).
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