Explanation Given: • Traffic flow rate: q ( t ) = 3000 + 2000 t − 300 t 2 • Time interval [ 8 , 10 ] Key Concepts Used: Many applications are based on the following principle. The net change in a quantity s ( t ) is equal to the integral of its rate of change: s ( t 2 ) − s ( t 1 ) = ∫ s ' ( t ) ⋅ d t t 1 t 2 . Here s ( t 2 ) − s ( t 1 ) is the net change in s ( t ) over the time interval [ t 1 , t 2 ] and ∫ s ' ( t ) ⋅ d t t 1 t 2 is Integral of rate of change. The number of cars per hour passing an observation point along a highway is called the traffic flow rate q ( t ) (in cars per hour) Here in the problem it is given that the traffic flow rate q ( t ) = 3000 + 2000 t − 300 t 2 .We have to find the number of cars pass overthe time interval [ 8 , 10 ] . We consider the initial time 8 AM as 0 for our convenience thereby the final time 10 AM should be 2 . The net change in number of cars over the time interval is given as ∫ q ( t ) ⋅ d t t 1 t 2 . Substitute the given values of time interval and the traffic flow rate, we can find the number of cars pass over the time interval [ 8 , 10 ] . Calculation: Description: Netchange in number of cars over a time interval [ t 1 , t 2 ] ∫ q ( t ) ⋅ d t t 1 t 2 = n ( t 2 ) − n ( t 1 ) w h e r e n ( t ) r e p r e s e n t s t h e n u m b e r o f c a r s ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Differential Equations

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Chapter 5.6, Problem 15E

To determine

Number of cars pass by in the given time interval for the provided traffic flow rate

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Chapter 5.6, Problem 14E

Chapter 5.6, Problem 16E

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Number of cars pass by in the given time interval for the provided traffic flow rate

Solution Summary: The author explains the traffic flow rate q (t) = 3000 + 2000 t 300

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