Police use the formula [math]v=2 \sqrt{5 L}[/math] to estimate the speed of a car, v, in miles per hour, based on the length, L, 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 car’s skid marks to be 45 feet long. Estimate the speed at which the motorist was traveling before braking. If the posted speed limit is 35 miles per hour and the motorist tells the officer she was not speeding, should the officer believe her? Explain

And if we compare this value with the speed limit of 35 mi/h then the police officer should believe that the motorist was not speeding, since his speed was lower than 35 mi/hr.

Step-by-step explanation:

Estimate the speed at which the motorist was traveling before braking

For this case we have the following formula for the spped of a car:

[tex] V= 2 \sqrt{5L}[/tex]

Where L represent the length and v the velocity in miles/hr.

For this case we know that a police officer measures the car’s skid marks to be 45 feet long, so then L =45 ft, and we can finde the velocity of the car replacing L=45 ft and we got:

[tex] V(L=45) = 2\sqrt{5*45ft}= 2 \sqrt{225}= 2*15 =30 \frac{mi}{hr}[/tex]

If the posted speed limit is 35 miles per hour and the motorist tells the officer she was not speeding, should the officer believe her? Explain

And if we compare this value with the speed limit of 35 mi/h then the police officer should believe that the motorist was not speeding, since his speed was lower than 35 mi/hr.