The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance 8 (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. (Round your coefficients to 3 decimal places.) Reaction Braking time distance B Driver sees Driver applies Car obstacle brakes stops Speed, v 20 40 60 100 Reaction Time 8.2 16.7 24.6 41.9 Distance, R 33.3 Braking Time 2.0 9.3 Distance, B 19.8 35.9 56.2 (@) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. R(v) = (b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance time B. B(v) = (c) Determine the polynomial giving the total stopping distance T. T(V ) = (d) Use a graphing utility to graph the functions R, B, and 7 in the same viewing window. B 60 100 120 80 160 120 X (e) Find the derivative of 7 and the rates of change of the total stopping distance for v = 40, v = 80, and v = 100. T(v) =