Question

The equation d=0.05v2+1.1v models the distance, d, that it takes are car traveling v miles per hour to come to a complete stop. If Hannah’s car stopped after travelling 250 feet on a highway with a speed limit of 65 mph, was Hannah speeding? Explain using math whether she was speeding and how you know.

Answer 1

Answer:

• Hannah was not speeding because her speed was about 61 mph, which is below the speed limit.

Explanation:

Just to correct some typos, this is the complete question:

The equation d=0.05v² +  1.1v models the distance, d, that it takes a car traveling at a speed of v miles per hour to come to a complete stop. If Hannah’s car stopped after travelling 250 feet on a highway with a speed limit of 65 mph, was Hannah speeding? Explain using math whether she was speeding and how you know.

Solution

To find whether Hannah was speeding, you must find the velocity that is solution for the equation:

• 250=0.05v² +  1.1v

Write it in standard form:

• 0.05v² +  1.1v - 250 = 0

Use the quadratic formula:

       $v=\dfrac{-1.1\pm\sqrt{(1.1)^2-4(0.05)(-250)}}{2(0.05)}$

      $v=\dfrac{-1.1\pm 7.1561}{0.1}$

       $v=60.6\text{ or }v=-82.6$

The speed can only be positive; thus, it is about 61 miles per hour, which is below the speed limit of 65mph.

In conclusion, she was not speeding.