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Chapter 8: Problem 23

Determine the traffic flow if 100 cars pass a known location during \(10 \mathrm{~s}\).

Short Answer

Expert verified
The traffic flow is 10 cars per second.

Step by step solution

01

Identify the Given Values

The problem gives the total number of cars, which is 100, and the time interval, which is 10 seconds.
02

Formula for Traffic Flow

Traffic flow (T), denoted as vehicles per unit time, can be calculated as the total number of vehicles (V) divided by the total time (t). So the formula for traffic flow (T) is \( T = \frac{V}{t} \).
03

Substitute the Given Values into the Formula

Substituting V = 100 cars and t = 10 seconds into the formula, the traffic flow rate \(T\) is found as follows: \(T = \frac{100}{10}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

vehicle count
When discussing traffic flow, the vehicle count is the total number of vehicles that pass a certain point on a road within a given time frame. In our example exercise, the vehicle count is provided as 100 cars. Counting vehicles helps traffic engineers understand the volume of traffic on a particular stretch of road.
Understanding vehicle count is essential for several reasons:
  • It provides insights into road congestion and helps identify busy routes.
  • Planners use vehicle counts to design better traffic control systems like traffic lights and signs.
  • It aids in predicting traffic patterns and managing the flow of vehicles efficiently.
By knowing how many vehicles pass a location, one can analyze and strategize to improve overall traffic management.
time interval
A time interval is the duration over which the vehicle count is measured. It is crucial because it stabilizes the measurement, making it meaningful and comparable. In the given exercise, the time interval is 10 seconds.
The use of a consistent time interval allows:
  • Standardized data collection, ensuring that all vehicle counts are comparable regardless of location or conditions.
  • A better understanding of traffic behavior over time, which assists in trend analysis and forecasting.
  • The ability to calculate average traffic flow, helping in identifying peak traffic periods.
Choosing an appropriate time interval is important as very short intervals might not capture the full picture, while very long intervals might miss variations in traffic flow.
flow rate formula
The flow rate formula is a pivotal tool in calculating how many vehicles pass through a point over a unit of time. It's represented as:\[ T = \frac{V}{t} \]where:
  • \(T\) is the traffic flow rate,
  • \(V\) is the vehicle count,
  • \(t\) is the time interval.
Understanding this formula is important:
  • It helps determine whether a road can handle current and future traffic volumes.
  • A consistent traffic flow calculation aids in designing infrastructure improvements.
  • This formula enables the easy conversion of observations into actionable data for traffic management.
In our exercise, substituting the known values (100 cars and 10 seconds) into the formula gives:\[ T = \frac{100}{10} = 10 \text{ cars per second} \]Thus, the flow rate tells us on average how many cars pass each second, a critical part of managing traffic effectively.

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