# Applied maths

| 0

## Chapter 1 The Profession of Transportation

1. What is the total number of miles of public roadways in your state? What percentage of the highway system mileage is maintained by the state government (as opposed to local and federal government)? What percentage of the total public highway system in your state is comprised of Interstate highways?

Note: These data are available from the Internet site of FHWA’s Office of Highway Policy Information at

http://www.fhwa.dot.gov/policyinformation/statisti…

1. Estimate the number of personal motor vehicles in your city or state. What is the total number of miles driven each year? How much revenue is raised per vehicle per year for each 1 cent/gallon tax? Assume that the average vehicle achieves 25 miles per gallon in fuel economy.
2. A state has a population of 17 million people and an average ownership of 1.1 cars per person, each driven an average of 12,000 mi/year, at an average fuel economy of 24 mi/gal of gasoline (mpg). Officials estimate that an additional \$60 million per year in revenue will be required to improve the state’s highway system, and they have proposed an increase in the gasoline tax to meet this need. Determine the required tax in cents per gallon.

### Chapter 2 Transportation Systems and Organizations

1. Abridgehasbeenconstructedbetweenthemainlandandanisland. The total cost (excluding tolls) to travel across the bridge is expressed as C = 50 + 0.5V, where V is the number of veh/hr and C is the cost/vehicle in cents. The demand for travel across the bridge is V = 2500 −10C.

2

(a) Determine the volume of traffic across the bridge.
(b) If a toll of 25 cents is added, what is the volume across the bridge? What volume would be expected with a 50 cent increase?
(c) A tollbooth is to be added, thus reducing the travel time to cross the bridge. The new cost function is C = 50 + 0.2V. Determine the volume of traffic that would cross the bridge.
(d) Determine the toll to yield the highest revenue for demand and supply function in part (a), and the associated demand and revenue.

1. Considerationisbeinggiventoincreasingthetollonabridgenow carrying 4500 veh/day. The current toll is \$1.25/veh. It has been found from past experience that the daily traffic volume will decrease by 400 veh/day for each 25¢ increase in toll. Therefore, if x is the increase in toll in cents/veh, the volume equation for veh/day is V = 4500 − 400 (x / 25), and the new toll/veh would be T = 125 + x. In order to maximize revenues, what would the new toll charge be per vehicle and what would the traffic in veh/day be after the toll increase?
2. An individual is planning to take an 600-mile trip between two large cities. Three possibilities exist: air, rail, or auto. The person is willing to pay \$25 for every hour saved in making the trip. The trip by air costs \$450 and travel time is 6 hrs, by rail the cost is \$400 and travel time is 10 hrs, and by auto the cost is \$250 and travel time is 15 hrs. (a) Which mode is the best choice?
(b) What factors other than cost might influence the decision regarding which mode to use?

#### Chapter 3 Characteristics of the Driver, Pedestrian, Bicyclist, Vehicle, and the Road

1. Thedesignspeedofamultilanehighwayis60mi/h.Determine(a)the minimum stopping sight distance that should be provided for a level roadway, and (b) the minimum stopping sight distance that should be provided for a roadway with a maximum grade of 7 percent.

3

Note: the term a/g in the appropriate equation is typically rounded to 0.35 for calculation purposes. Assume perception reaction time = 2.5 sec.

1. The acceleration of a vehicle can be expressed as: du/dt = 3.6 – 0.06u If the vehicle speed, u, is 30 ft/sec at time T0, Determine: (a) Distance traveled when the vehicle has accelerated to 45 ft/sec. (b) Time for vehicle to attain the speed of 45 ft/sec.
(c) Acceleration after 4 seconds.
2. Determine the horsepower developed by a passenger car traveling at a speed of 50 mi/h on an upgrade of 5% with a smooth pavement. The weight of the car is 3500 lb and the cross-sectional area of the car is 40 ft2.
1. A driver on a level two-lane highway observes a truck completely blocking the highway. The driver was able to stop her vehicle only 30 ft from the truck. If the driver was driving at 55 mi/h, how far was she from the truck when she first observed it (assume perception-reaction time is 1.5 seconds)? How far was she from the truck at the moment the brakes were applied (use a/g = 0.35)?

Last Updated on February 11, 2019