Question

The distance required for a car to come to a stop after its brakes are

applied is directly proportional to the square of its speed. If the stopping distance
for a car traveling 35 miles per hour is 26 feet, what is the stopping distance for a
car traveling 65 miles per hour? Round to two decimal places and label your answer.

Answer 1

Explanation:

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