Question 3: (a) A section of highway is known to have a free-flow speed of 95 km/h and a capacity of 3300 veh/h. Your summer student indicates that the average time in between passing vehicles was 1.6 seconds during an hour of monitoring If the linear speed-density relationship applies, what was the space-mean speed of the vehicles during the hour of monitoring?
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- Data obtained from aerial photography showed nine vehicles on a 720 ft-long section of road. Traffic data collected at the same time indicated an average time headway of 4.2 sec. Determine the following. (a) the density on the highway (in veh/mi) veh/mi (b) the flow on the road (in veh/h) veh/h (c) the space mean speed (in mi/h) mi/hConsider only a single lane of a highway. Based on extensive data from an urban freeway it is assumed thatfree-flow speeds (i.e., there are no jams) can best be represented by a Normal distribution with mean andstandard deviation 119 km/h and 13.1 km/h, respectively.1. What is the probability that the speed of a randomly selected vehicle is between 100 and 120 km/h?2. What is the expected number of vehicles between two vehicles that exceed the posted speed limit of100 Km/h? You can use the Z table for calculating the final answer. You can also write your final answer in form ofR functions or as PDF/CDF of statistical distributions with correct arguments.The median speed of vehicles on a highway segment during rush hour is 40 mph with Cv of 0.2. Assuming lognormal distribution, find the fraction of time the speed will fall below 10 mph? What about greater than 50 mph?
- A vehicle pulls out onto a single-lane highway that has a flow rate of 300 veh/h (Poisson distributed). The driver of the vehicle does not look for oncoming traffic. Road conditions and vehicle speeds on the highway are such that it takes 1.7 seconds for an oncoming vehicle to stop once the brakes are applied. Assuming a standard driver reaction time of 2.5 seconds, what is the probability that the vehicle pulling out will get in an accident with oncoming traffic?Assume you are an observer standing at a point on a three lane race track. All vehicles in lane 1 are traveling at 50 mi/h, all vehicles in lane 2 are traveling at 65 mi/h, and all vehicles in lane 3 are traveling at 70 mi/h. There is a constant spacing of 0.25 mile. If you collect spot speed data for all vehicles that pass your observation point in one hour, what will the time-mean speed be for the traffic stream?Data obtained from aerial photography showed six vehicles on a 200 metre long section of road. Traffic data collected at the same time indicated an average time headway of 4 sec. Determine (a) the density on the highway, (b) the flow on the road, and (c) the space mean speed.
- Two sets of students are collecting traffic data at two sections, xx and yy, of a highway 1,200 ft apart. Observations at xx show that five vehicles passed that section at intervals of 3, 4, 3, and 5 sec, respectively. If the speeds of the vehicles were 55, 50, 45, 40, and 35 mi/h, respectively, determine the space mean speed (in km/h) for the data using the following equation where ut and us are in km/h. (Round your answer to at least three significant figures.) ut = 0.966us + (3.541 km/h) km/h Determine the space mean speed (in km/h) for the data using the following equation. (Round your answer to at least three significant figures.) us = n n 1 ui i=1 km/h Compare your answers and discuss the results.A researcher was positioned at the side of a 2-lane rural highway. He recorded the volume of northbound traffic, aggregated into 15 minute intervals. The recorded volumes were 243, 276, 318 and 490 vehicles for the first, second, third, and fourth 15-minute intervals, respectively. Calculate the peak flow rate (v/h). Provide your answer to the nearest integer.An observer counts 360 veh/h at a specific highway location. Assuming that the arrival of vehicles at this highway location is Poisson distributed, estimate the probabilities of having at most 3 vehicles arriving over a 20-second time interval . choices: 74.29%, 85.71%, 93.23%, 67.66%
- A data collection study found a linear speed - density relationship for a highway as follows u/65 +k/120 =1 1-Write down the speed - density ( given ) , flow - density and flow - speed models , and plot their relationships 2-raffic study has shown that the time headways between successive vehicles on this highway are exponentially distributed and that 30% of the headways between vehicles are 4 seconds or greater. Apply the traffic models derived in the question a), compute speeds and densities corresponding to this flow.In a stream of vehicles, 20% of the vehicles travel at a constant 50 km/hr, 30% at a constant speed of 80 km/hr and the remaining vehicles travel at a constant speed of 100 km/hr. An observer travelling at a constant speed of 60 km/hr over a length of 6 km with the stream is passed by 10 more vehicles than he passes. When the observer travels against the stream at the same speed and over the same length of highway, the number of vehicles met is 390. What is the mean speed and flow of traffic stream being observed? How many vehicles travelling at 100 km/hr are met by the observer while he travels against the stream?A section of a highway is known to have a free-flow speed of 65 mi/h and a capacity of 3500veh/h. In a given hour, 2500 vehicles were counted at a specified point along this highway section. If the linear speed-density relationship applies. What would you estimate the space-mean speed (mph) of these 2500 vehicles be? choices: 50.34, 48.61, 49.87, 51.46