Chapter 3.2, Problem 144E

Braking Distance Braking distance for cars on level pavement can be approximated by $D(x)=\frac{x^2}{30k},$ The input x is the car's velocity in miles per hour and the output D(x) is the braking distance in feet. The positive constant k is a measure of the traction of the tires. Small values of k indicate a slippery road or worn tires.

(Source: L. Haefner, Introduction to Transportation Systems.)

(a) Let k = 0.3. Evaluate D(60) and interpret the result.

(b) If k = 0.25, find the velocity x that corresponds to a braking distance of 300 feet.