Question

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.

Answer 1

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
 Answer:
 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