Modeling Braking Distance for a Car
On wet, level pavement highway engineers sometimes model the braking
distance in feet for a car traveling at x miles per hour using:
(Source: L. Haefner, Introduction to Transportation Systems.)
a). Evaluate f(30) and f(60). Interpret the results.
Solution to part a):
To evaluate f(30) substitute 30 for x into function f. So . Thus, when the car is traveling 30 miles per hour, the braking distance is 100 feet.
To evaluate f(60) replace x with 60. So . Thus, when the car is traveling 60 miles per hour, the braking distance is 400 feet.
Solution to part b).
The average rate of change from 30 to 60 is
Thus, for each 1 mile per hour increase in speed between 30 and 60, the increase in braking distance is, on average, 10 feet.
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