The stopping distance of an automobile is directly proportional to the square of its speed v. a car required 90 feet to stop when its speed was 70 miles per hour. find a mathematical model that gives the stopping distance d in terms of its speed v. estimate the stopping distance if the brakes are applied when the car is traveling at 71 miles per hour.

First we write the mathematical model in a generic way:
 "The stopping distance of an automobile is directly proportional to the square of its speed v"
 d = kv ^ 2
 Where,
 k: proportionality constant.
 We now look for the value of K:
 d = kv ^ 2
 90 = k ((70) * (5280/3600)) ^ 2
 k = 90 / ((70) * (5280/3600)) ^ 2
 k = 0.008538539 s ^ 2 / feet
 The equation will then be:
 d = (0.008538539) * v ^ 2
 For v = 71 miles per hour we have:
 d = (0.008538539) * ((71) * (5280/3600)) ^ 2
 d = 92.6 feet
 
 a mathematical model that gives the stopping distance in terms of its speed v is:
 d = (0.008538539) * v ^ 2
 The stopping distance if the brakes are applied when the car is traveling at 71 miles per hour is:
 d = 92.6 feet