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

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

• A. Flow rate equals distance traveled per time
• B. q = k * V
• C. Density equals speed plus flow rate
• D. Speed equals flow rate times density

Answer: (B)

Flow is the rate at which vehicles pass a point, and it comes from how many vehicles occupy a given stretch of road (density) and how fast they move (speed). The fundamental relationship expresses this as flow equals density times speed: q = k × V. In consistent units, density k is vehicles per kilometer and speed V is kilometers per hour, so their product gives flow q in vehicles per hour. This captures the intuition that increasing either the number of vehicles on the road or their speed increases how many vehicles pass a point each hour. The other options don’t fit: flow described as distance traveled per time is just speed; density equal to speed plus flow rate mixes incompatible quantities; and speed equal to flow rate times density would give incorrect units for velocity.

Flow is the rate at which vehicles pass a point, and it comes from how many vehicles occupy a given stretch of road (density) and how fast they move (speed). The fundamental relationship expresses this as flow equals density times speed: q = k × V. In consistent units, density k is vehicles per kilometer and speed V is kilometers per hour, so their product gives flow q in vehicles per hour. This captures the intuition that increasing either the number of vehicles on the road or their speed increases how many vehicles pass a point each hour. The other options don’t fit: flow described as distance traveled per time is just speed; density equal to speed plus flow rate mixes incompatible quantities; and speed equal to flow rate times density would give incorrect units for velocity.