PEC EPE Exam Numerical Questions for Civil / Transportation Engineering
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A vehicle travels a distance of 240 km in 4 hours. What is its average speed?
Solution:
Average speed = Total distance / Total time
Average speed = 240 km / 4 hours
Average speed = 60 km/h
A bus starts from a station and travels at an average speed of 40 km/h for 2 hours. It then increases its speed to 60 km/h for the next 3 hours. What is the total distance covered by the bus?
Solution:
Distance covered in the first 2 hours = 40 km/h * 2 hours = 80 km
Distance covered in the next 3 hours = 60 km/h * 3 hours = 180 km
Total distance covered = 80 km + 180 km = 260 km
The traffic flow on a highway is measured as 1500 vehicles per hour. If the average vehicle length is 5 meters, what is the flow rate in vehicles per minute?
Solution:
Flow rate in vehicles per minute = Traffic flow in vehicles per hour / 60
Flow rate in vehicles per minute = 1500 vehicles per hour / 60 = 25 vehicles per minute
A freight train takes 3 minutes to pass completely through a tunnel. If the length of the train is 250 meters, what is the speed of the train?
Solution:
Speed = Distance / Time
Speed = 250 meters / 3 minutes = 83.33 meters per minute
The stopping sight distance for a vehicle traveling at 60 km/h is 60 meters. If the perception-reaction time of the driver is 2 seconds, what is the total stopping distance for the vehicle?
Solution:
Total stopping distance = Perception-reaction distance + Braking distance
Perception-reaction distance = (Perception-reaction time) * (Speed in m/s)
Perception-reaction distance = 2 seconds * (60 km/h * 1000 m/km) / (3600 s/h) = 33.33 meters
Braking distance = Stopping sight distance – Perception-reaction distance
Braking distance = 60 meters – 33.33 meters = 26.67 meters
Total stopping distance = 33.33 meters + 26.67 meters = 60 meters
A traffic signal operates with a cycle length of 120 seconds. If the green time for a particular movement is 40 seconds, what is the time for which this movement is stopped (red time)?
Solution:
Red time = Cycle length – Green time
Red time = 120 seconds – 40 seconds = 80 seconds
A city has a total road network of 800 kilometers and an annual traffic growth rate of 5%. What is the increase in road length after 4 years?
Solution:
Increase in road length = Initial road length * (Growth rate/100) * Number of years
Increase in road length = 800 km * (5/100) * 4 years = 160 km
The annual average daily traffic (AADT) on a highway is 10,000 vehicles. If the design period is 20 years and the traffic growth rate is 3% per year, what will be the traffic volume after 20 years?
Solution:
Traffic volume after 20 years = AADT * (1 + Growth rate/10e0)^Number of years
Traffic volume after 20 years = 10,000 * (1 + 3/100)^20 ≈ 18,061 vehicles
A road has a width of 7 meters and consists of two lanes. If each lane has a width of 3.5 meters, what is the total paved area of the road (excluding shoulders) for a length of 2 kilometers?
Solution:
Total paved area = Road width * Length
Total paved area = (2 lanes * 3.5 meters) * 2000 meters = 14,000 square meters
The traffic flow on a road segment is measured as 800 vehicles per hour. If the average headway (time gap between consecutive vehicles) is 5 seconds, what is the flow rate in vehicles per second?
Solution:
Flow rate in vehicles per second = Traffic flow in vehicles per hour / 3600
Flow rate in vehicles per second = 800 vehicles per hour / 3600 = 0.22 vehicles per second
A traffic signal at an intersection has a cycle length of 120 seconds. The green time for the main road is 40 seconds, and the green time for the left-turn movement is 30 seconds. Calculate the total lost time at the intersection.
Solution:
Total lost time = Cycle length – (Green time for main road + Green time for left-turn movement)
Total lost time = 120 seconds – (40 seconds + 30 seconds) = 50 seconds
The width of a two-lane highway is 7 meters, and each lane has a width of 3.5 meters. If the shoulder width on each side is 1 meter, calculate the total width of the road including the shoulders.
Solution:
Total width of the road = (Width of two lanes + Shoulder width on one side + Shoulder width on the other side)
Total width of the road = (2 lanes * 3.5 meters) + (1 meter + 1 meter) = 9 meters
The sight distance required for a vehicle traveling at 80 km/h is 100 meters. If the perception-reaction time of the driver is 2 seconds, calculate the stopping distance for the vehicle.
Solution:
Stopping distance = Sight distance required + Perception-reaction distance
Perception-reaction distance = (Perception-reaction time) * (Speed in m/s)
Perception-reaction distance = 2 seconds * (80 km/h * 1000 m/km) / (3600 s/h) ≈ 44.44 meters
Stopping distance = 100 meters + 44.44 meters ≈ 144.44 meters
A road segment has a traffic flow rate of 1,200 vehicles per hour. If the average headway (time gap between consecutive vehicles) is 5 seconds, calculate the speed at which the vehicles are traveling.
Solution:
Speed = Distance / Time
Distance = Length of each vehicle
Time = Average headway = 5 seconds
Speed = Length of each vehicle / Average headway
Speed = 5 meters / 5 seconds = 1 meter per second
A bus travels at an average speed of 50 km/h for a distance of 200 kilometers. Calculate the travel time for the bus.
Solution:
Travel time = Distance / Average speed
Travel time = 200 km / 50 km/h = 4 hours
The demand for a transportation service is 1,500 trips per day. If the service operates for 16 hours per day, calculate the average flow rate of trips per hour.
Solution:
Average flow rate = Demand / Operating hours per day
Average flow rate = 1,500 trips / 16 hours = 93.75 trips per hour
The critical headway for a traffic signal is 5 seconds. If the saturation flow rate at the intersection is 1,800 vehicles per hour, calculate the cycle length of the traffic signal.
Solution:
Cycle length = Critical headway * Saturation flow rate
Cycle length = 5 seconds * (1,800 vehicles per hour / 3600 seconds per hour) = 2.5 seconds
The traffic flow on a highway is measured as 2,000 vehicles per hour. If the average vehicle length is 4 meters, calculate the density of vehicles on the highway in vehicles per kilometer.
Solution:
Density = Traffic flow / Speed
Density = 2,000 vehicles per hour / (80 km/h * 1000 m/km) = 0.025 vehicles/meter
Density in vehicles per kilometer = 0.025 vehicles/meter * 1000 meters/km = 25 vehicles/km
The stopping sight distance required for a vehicle is 80 meters. If the initial speed of the vehicle is 100 km/h, calculate the minimum deceleration rate needed to stop the vehicle within the sight distance.
Solution:
Speed = Initial speed = 100 km/h
Stopping sight distance = 80 meters
Deceleration rate = (Initial speed)^2 / (2 * Stopping sight distance)
Deceleration rate = (100 km/h)^2 / (2 * 80 meters) ≈ 125 km/h^2 ≈ 34.72 m/s^2
A highway segment has a flow rate of 1,500 vehicles per hour and an average vehicle speed of 60 km/h. Calculate the density of vehicles on the highway in vehicles per kilometer.
Solution:
Density = Traffic flow / Speed
Density = 1,500 vehicles per hour / (60 km/h * 1000 m/km) = 0.025 vehicles/meter
Density in vehicles per kilometer = 0.025 vehicles/meter * 1000 meters/km = 25 vehicles/km