MATH 1101: Modeling Breaking Distance of a Car

Modeling Braking Distance for a Car

The Problem

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.
b). Calculate the average rate of change of f from 30 to 60. Discuss what the results mean.

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.