Homework SourseFor several weeks the highway department has been recording
For several weeks, the highway department has been recording the speed of freeway traffic flowing past a certain downtown exit. The data suggest that between the hours of 1:00 and 6:00 P.M. on a normal weekday, the speed of traffic at the exit is approximately
S(t) = t^3 - 10.5t^2 +30t - 26 miles per hour, where t is the number of hours past noon.
a. Compute the average speed of the traffic between the hours of 1:00 and 6:00 P.M.
b. At what time between 1:00 and 6:00 P.M. is the traffic speed at the exit the same as the average
speed found in part (a)? Round answer to one decimal place.
Please show calculations
S(t) = t^3 - 10.5t^2 +30t - 26 miles per hour, where t is the number of hours past noon.
a. Compute the average speed of the traffic between the hours of 1:00 and 6:00 P.M.
b. At what time between 1:00 and 6:00 P.M. is the traffic speed at the exit the same as the average
speed found in part (a)? Round answer to one decimal place.
Please show calculations
Solution
S(t)= t^3 - 10.5t^2 + 30t + 20 miles per hour Integrate above wrt t and put limits( 1 to 6) =193.75 a) -33.75 / 5 = -6.75 miles/hour b) -6.75 =t^3 - 10.5t^2 + 30t - 26 t = 0.9 hours and 3.5 hours (b) At times 01:54 and 04:30, speed of exit is same as average
