Question

police use the function ( f(x)=sqrt{20 x} ) to estimate the speed of a car, ( f(x) ), in miles per hour, based on the length, ( x ), in feet, of its skid marks upon sudden braking on a dry asphalt road. a motorist is involved in an accident. a police officer measures the cars skid marks to be 80 feet long. estimate the speed at which the motorist was traveling before braking. if the posted speed limit is 50 miles per hour and the motorist tells the officer he was not speeding, should the officer believe him? explain.
the car was traveling at ( square )

Explanation:

Step1: Substitute \(x = 80\) into the function

Given the function \(f(x)=\sqrt{20x}\), when \(x = 80\), we have \(f(80)=\sqrt{20\times80}\).

Step2: Simplify the expression inside the square - root

First, calculate \(20\times80=1600\). So \(f(80)=\sqrt{1600}\).

Step3: Evaluate the square - root

Since \(\sqrt{1600}=40\) (because \(40\times40 = 1600\)).

Answer:

The speed of the car was \(40\) miles per hour. Since \(40<50\), the officer should believe the motorist.