GATE 2024 CE (CE1) – Question 63

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 2 marks · Numerical answer

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: distance (0 to 500 m) against time (0 to 30 s). The vehicle trajectories are straight lines: (1) from (0 s, 400 m) to (10 s, 500 m); (2) from (0, 250) to (15, 500); (3) from (0, 100) to (30, 500); (4) from (5, 0) to (30, 400); (5) from (15, 0) to (30, 350); (6) from (20, 0) to (30, 150).]

The mean speed (in km/hr) of the vehicles in the entire time-space domain is _______________ (rounded off to the nearest integer).

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Correct answer: 57

Explanation

In the time-space domain the mean speed is the total distance travelled by all vehicles divided by the total time they spend in the domain. The distances are 100, 250, 400, 400, 350 and 150 m, a total of 1650 m. The times are 10, 15, 30, 25, 15 and 10 s, a total of 105 s. The mean speed is $\frac{1650}{105} = 15.71$ m/s $= 56.6$ km/h, which is 57 km/h.