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This calculation of flow, based on speed and separation, stands as a fairly fundamental relation, so let's do another other example.  In heavy traffic, speeds might be down to 10 miles per hour, with an average front-to-front distance of 45 feet.  Now 10 miles per hour equates to 15 feet a second, and with 45 foot spacing, we have a car every three seconds.  That again gives a flow of 1200 cars per hour per lane.

Of interest, the flow for the "light" early morning traffic and the "heavy" rush hour traffic equal.  So "heavy" traffic here more accurately represents "slow" traffic, since from a traffic flow viewpoint, our two examples give the same number.  Thus neither is actually "heavy" or "light" relative to each other.

Deceleration gets a bit trickier, but not too much so.  Let's take two cars, travelling 65 mile per hour, separated by some distance (not critical yet). And the first car slows at a half "g," or about 15 feet per second per second.  The trailing driver takes a second to react, before starting to slow.  In that second, the trailing car closes on the leading car by 7.5 feet.

How do we calculate that?

When the lead car starts to slow, both cars are traveling at 100 feet per second.  With a deceleration of 15 feet per second per second, the lead car, in the one second of reaction time, slows to 85 feet per second.  Given a smooth deceleration, the average speed of the lead car during that second was the average of the initial speed of 100 and the speed after one second of deceleration, or 85 feet per second.  That averages to 92.5 feet per second.  The trailing car traveled 100 feet during the reaction time, while the lead car traveled only 92.5 feet.  This gives a closing distance of the trailing car on the lead car at 7.5 feet.

If the trailing car takes two second to react, the trailing car closes 30 feet in the two seconds of reaction time, i.e. not twice the distance but four times the distance.  This occurs because the lead car slows to 70 feet per second in the two seconds.  The lead car travels at an average of 85 feet per second (the average of 100 at the beginning and 70 at the end of two seconds), or 170 feet across two seconds.  The lead car continued at 100 feet per second for two seconds, traveling 200 feet, bringing it 30 feet closer to the lead car.

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