GATE CE 2024 Set 1 — Question 63
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Transportation Engineering → Traffic Studies & Flow → Speed Studies
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Question
The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents unique identification of each vehicle.(Figure NOT to scale)
The mean speed (in km/hr) of the vehicles in the entire time-space domain is ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
```
The mean speed (in km/hr) of the vehicles in the entire time-space domain is ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
```
Correct answer
54 to 58
Solution
The mean speed is calculated as the total distance traveled by all vehicles divided by the total time spent by all vehicles.
From the graph:
Vehicle 1: Distance = 500 m, Time = 30 s
Vehicle 2: Distance = 500 m, Time = 25 s
Vehicle 3: Distance = 500 m, Time = 20 s
Vehicle 4: Distance = 300 m, Time = 30 s
Vehicle 5: Distance = 300 m, Time = 25 s
Vehicle 6: Distance = 300 m, Time = 20 sTotal distance traveled = m
Total time spent = sMean speed (m/s) = Convert to km/hr:
Mean speed (km/hr) =
Mean speed (km/hr) = Rounded off to the nearest integer, the mean speed is 58 km/hr.
From the graph:
Vehicle 1: Distance = 500 m, Time = 30 s
Vehicle 2: Distance = 500 m, Time = 25 s
Vehicle 3: Distance = 500 m, Time = 20 s
Vehicle 4: Distance = 300 m, Time = 30 s
Vehicle 5: Distance = 300 m, Time = 25 s
Vehicle 6: Distance = 300 m, Time = 20 sTotal distance traveled = m
Total time spent = sMean speed (m/s) = Convert to km/hr:
Mean speed (km/hr) =
Mean speed (km/hr) = Rounded off to the nearest integer, the mean speed is 58 km/hr.
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