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Emma H
Guest
Mathematical models of traffic flow can help to show how to avoid holdups and to ensure optimum flow conditions in congested situations such as road tunnels. A simple model for the flow rate F of cars along a straight level road is
F= v/L+vT + (v^2/ 2a)
where v is the speed of the cars, L is a car length (all cars are assumed to have the same length), a is the maximum deceleration of a car and T is the thinking time of a driver. Typical values of L, T and a are 4m, 0.8s and 7ms-2 respectively.
(ii) With the help of differential calculus, find the speed v which gives a maximum flow rate. (You may assume there is no minimum flow rate for v 0).
(iii) Given that 1 mile = 1609.344m, convert the previous answer from metres per second to miles per hour (nearest whole number).
Additional Details
I know its using the qoutient rule but thats when i get stuck it just doesnt seem to work for me!
F= v/L+vT + (v^2/ 2a)
where v is the speed of the cars, L is a car length (all cars are assumed to have the same length), a is the maximum deceleration of a car and T is the thinking time of a driver. Typical values of L, T and a are 4m, 0.8s and 7ms-2 respectively.
(ii) With the help of differential calculus, find the speed v which gives a maximum flow rate. (You may assume there is no minimum flow rate for v 0).
(iii) Given that 1 mile = 1609.344m, convert the previous answer from metres per second to miles per hour (nearest whole number).
Additional Details
I know its using the qoutient rule but thats when i get stuck it just doesnt seem to work for me!