Final answer:
To maximize the flow rate on a congested roadway, the derivative of the flow rate function F with respect to the speed v must be calculated, set to zero, and solved for 'v'.
Step-by-step explanation:
To find the speed that maximizes the flow rate on a congested roadway, we need to analyze the given function F = v / (22 + 0.02v^2). Maximizing the flow rate, in this context, implies finding the maximum point on the graph of this function, which essentially requires finding the derivative of the function and setting it to zero to solve for 'v'. This process is rooted in calculus, specifically in finding critical points.
First, we must calculate the derivative of the flow rate with respect to speed. Once we have the derivative, we set it equal to zero and solve for 'v'. This value of 'v' will be the speed that maximizes the flow rate, given there are no constraints on the speed such as speed limits or minimum speed requirements.
The act of finding the optimal speed to maximize flow rates essentially tackles a common problem in traffic engineering where understanding and optimizing vehicular movement is essential for minimizing congestions and improving road safety and efficiency.