Modeling Data
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 die distance B (in meters)the car travels after the brakes are applied (see figure).The table shows the results of an experiment.
Speed, v | 20 | 40 | 60 | 80 | 100 |
Reaction Time Distance, R | 8.3 | 16.7 | 25.0 | 33.3 | 41.7 |
Braking Time Distance, B | 2.3 | 9.0 | 20.2 | 35.8 | 55.9 |
(a) Use the regression capabilities of a graphing utility to find a linear model for reaction time distance R.
(b) Use the regression capabilities of a graphing utility to find a quadratic model for braking time distance B.
(c) Determine the polynomial giving the total stopping distance T.
(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 rates of change of the total stopping distance for v = 40, v = 80, and v = 100.
(f) Use the results of this exercise to draw conclusions about the total stopping distance as speed increases.
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Calculus of a Single Variable
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