The police department must determine a safe speed limit on a bridge so that the

Question

The police department must determine a safe speed limit on a bridge so that the flow rate of cars is at a maximum per unit time. The greater the speed limit, the farther apart the cars must be expected to be in order to allow for a safe stopping distance. The total distance needed for a car to stop, if a car in front of it stops suddenly, depends on two factors: time needed to react and the speed of the car. Experimental data on the stopping distance d (in feet), on the bridge surface, for various speeds s (in miles per hour) is given in the following table. The table also provides an estimate for reaction distance r (in feet); this is the distance the car will travel before the driver reacts. s(in mph): 5, 10, 20, 30, 40, 50, 60 d(in feet): 4, 11, 33, 62, 100, 149, 203 r(in feet): 5, 10, 20, 30, 40, 50, 60 The police department has also identified the lengths of the 5 most common types of vehicles that are expected to use the bridge: Model, Length (in inches): Fiat 500: 142 Ford: 153.1 Dodge: 173.8 Honda: 176.5 Dodge Caravan: 202.5 The bridge will also be used occasionally by tractor-trailers with an average length of 75 feet and stopping distances that are about 40% greater than the stopping distances for an automobile. 1. Find a function of the form d(s) = as2 + bs + c that models the stopping distance in terms of speed. What should d(0) equal? What is a reasonable estimate for d?(0)? Select the constants a, b and c that best fits the data and produces the value of d(0) and d?(0) that you identified. 2. Produce a model for the flow rate of the cars crossing the bridge. Consider two consecutive cars each with vehicle length l and traveling a speed s. If the driver in the second car is traveling a safe distance from the first car (i.e. allowing enough time to react and stop if the first brakes suddenly), what is the distance between the cars? How much time elapses between the moment the front bumper of the first car enters the bridge to the moment the front bumper of the second car enters the bridge? Find a formula in terms of s the provides the number of cars that enter the bridge per minute, assuming each car is the same length and there is the same (safe) distance between each car. 3. Assuming all the cars have vehicle length l, what should be the speed limit (in miles per hour) in order to maximize traffic flow? Provide a graph of this optimal speed limit in terms of the vehicle length l. How does the vehicle length affect the optimal speed limit? What should the speed limit on the bridge be to safely accommodate the 5 most common vehicle types expected to use the bridge. 5. What should be the speed limit if the stopping distance and length of tractor-trailers is also taken into account?

Explanation / Answer

Can someone please answer this please?

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.