Modeling Data The slopping disiance of an aiitoniohilc traveling at a speed i'

Chapter 2, Problem 99

(choose chapter or problem)

Modeling Data The slopping disiance of an aiitoniohilc traveling at a speed i' (kiloineteis per hour) is the distanee R (meters) the car travels during the reaction time of the driver plus the distance B (meters) the car travels after the brakes are applied (see figure). The table shows the results of an experniienl. Reaction time Stopping distance t R t B g Driver sees Driver applies Car obstacle hrakes stops V 20 40 60 80 100 R 3.3 6.7 10.0 13.3 16.7 B -) -i^ 8.9 20.2 35.9 56.7 (a) Use the regression capabiHties of a graphing utilit\ to lind a linear model for reaction lime, (bl Use the regression capabilities of a graphing utilit\ to find a quadratic model for braking time, (cl Determine the polynomial gi\'ing the total stopping distance I . (d) Use a graphing utility to graph the functions R. B. and T in the same viewing window. (e) Find the derivative of T and the rate of change of the total stopping distance for r = 40. r = 80, and r = 100, (fl Use the results of this exercise to draw conclusions about the total stopping distance as speed increases,