Functional-Dependency
October 31, 2024STQC-NIELIT SC-B 2021
November 1, 2024TIFR PHD CS & SS 2019
| Question 8 |
Consider the following toy model of traffic on a straight, single lane, highway. We think of cars as points, which move at the maximum speed v that satisfies the fol- lowing constraints:
1. The speed is no more than the speed limit vmax mandated for the highway.
2. The speed is such that when travelling at this speed, it takes at least time t0 (where t0 is a fixed time representing the reaction time of drivers) to reach the car ahead, in case the car ahead stops suddenly.
Let as assume that in the steady state, all cars on the highway move at the same speed v satisfying both the above constraints, and the distance between any two successive cars is the same. Let ρ denote the “density”, that is, the number of cars per unit length of the highway. Which of the following graphs most accurately captures the relationship between the speed v and density ρ in this model?
1. The speed is no more than the speed limit vmax mandated for the highway.
2. The speed is such that when travelling at this speed, it takes at least time t0 (where t0 is a fixed time representing the reaction time of drivers) to reach the car ahead, in case the car ahead stops suddenly.
Let as assume that in the steady state, all cars on the highway move at the same speed v satisfying both the above constraints, and the distance between any two successive cars is the same. Let ρ denote the “density”, that is, the number of cars per unit length of the highway. Which of the following graphs most accurately captures the relationship between the speed v and density ρ in this model?
| a | |
| b | |
| c | |
| d | |
| e |
Correct Answer: C
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