Wednesday
September 17, 2014

Homework Help: Calculus

Posted by Max on Friday, November 9, 2012 at 2:51pm.

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 the speed of the car through two factors: the time needed to react and the braking distance. Experimental data on the braking 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 500 142.0
Ford Fiesta 153.1
Dodge Caliber 173.8
Honda Civic 176.5
Dodge Grand 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 breaking distance in terms of speed s. 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. Also find a function r(s) that models the reaction distance in terms of the
speed.
Please Help!!!!!

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