SOLUTION: A car with good tire tread can stop in less distance than a car with poor tread. The formula for the stopping distance d, in feet, of a car with good tread on dry cement is approxi

Question 1204951: A car with good tire tread can stop in less distance than a car with poor tread. The formula for the stopping distance d, in feet, of a car with good tread on dry cement is approximated by
d = 0.04v2 + 0.5v,
where v is the speed of the car. If the driver must be able to stop within 74 ft, what is the maximum safe speed, to the nearest mile per hour, of the car?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A car with good tire tread can stop in less distance than a car with poor tread. The formula for the stopping distance d, in feet, of a car with good tread on dry cement is approximated by
d = 0.04v2 + 0.5v,
where v is the speed of the car. If the driver must be able to stop within 74 ft, what is the maximum safe speed, to the nearest mile per hour, of the car?
-----------------
d = 0.04v^2 + 0.5v = 74
v^2 + 12.5v - 1850 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=7556.25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 37.2133466267843, -49.7133466267843. Here's your graph:

Ignore the negative result
v = 37 mi/hr

RELATED QUESTIONS
A car with good tire tread can stop in less distance than a car with poor tread. The... (answered by jorel1380)

A new set of car tires has a tread depth of 8 millimeters. The tread depth decreases... (answered by oberobic)

The stopping distance D of a car after the brakes are applied varies directly as the... (answered by checkley77)

The stopping distance D of a car after the brakes are applied varies directly as the... (answered by ankor@dixie-net.com)

Hi. May I have some help with the following problem? For a certain model of car the... (answered by checkley71,solver91311)

To stop a moving car takes some time and distance. The stopping distance d of a car... (answered by Theo)

The formula d = 0.05s^2 + 1.1s estimates the minimum stopping distance d in feet for a... (answered by checkley71)

In a study, nine tires of a particular brand were driven on a track under identical... (answered by Theo)

For a certain model of car the distance d required to stop the vehicle if it is traveling (answered by math_tutor2020)