Which equation expresses the fundamental relationship among flow, speed, and density in traffic flow theory?

Which equation expresses the fundamental relationship among flow, speed, and density in traffic flow theory?

• A. The maximum discharge rate from an approach when queues are present and the signal is green.
• B. q = v × k
• C. q = v / k
• D. q = v + k

Answer: (B)

The main idea being tested is how flow, speed, and density relate to each other. In traffic flow, flow (the number of vehicles passing a point per unit time) is the product of how fast vehicles are moving and how densely packed they are. So the fundamental relationship is q = v × k, where q is flow, v is speed, and k is density. If you know the density and the speed, you can predict how many vehicles pass a point each second or hour. For example, keeping speed the same, increasing density means more vehicles pass per unit time, so flow rises linearly with density. If density is fixed and speed increases, flow also goes up. In the extreme cases, if there are no vehicles (density is zero) or they aren’t moving (speed is zero), the flow is zero. The units check out: with v in miles per hour (or meters per second) and k in vehicles per mile (or per meter), their product gives vehicles per hour (or per second). Other options don’t express the fundamental link among the three quantities. The first choice describes a capacity or saturation scenario, not the basic relationship, and the remaining formulas don’t combine speed and density in a way that yields flow with consistent units.

The main idea being tested is how flow, speed, and density relate to each other. In traffic flow, flow (the number of vehicles passing a point per unit time) is the product of how fast vehicles are moving and how densely packed they are. So the fundamental relationship is q = v × k, where q is flow, v is speed, and k is density.

If you know the density and the speed, you can predict how many vehicles pass a point each second or hour. For example, keeping speed the same, increasing density means more vehicles pass per unit time, so flow rises linearly with density. If density is fixed and speed increases, flow also goes up. In the extreme cases, if there are no vehicles (density is zero) or they aren’t moving (speed is zero), the flow is zero. The units check out: with v in miles per hour (or meters per second) and k in vehicles per mile (or per meter), their product gives vehicles per hour (or per second).

Other options don’t express the fundamental link among the three quantities. The first choice describes a capacity or saturation scenario, not the basic relationship, and the remaining formulas don’t combine speed and density in a way that yields flow with consistent units.