Police use the formula: \( v=\sqrt{20 L} \) to estimate the speed of a car, \( v \), in miles per hour, based on the length, \( L \), in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 115 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit. Answer: The car was traveling at approximately miles per hour.

To find the speed of the car, we can plug the length of the skid marks into the formula \( v = \sqrt{20 L} \). Given \( L = 115 \) feet, we have: \[ v = \sqrt{20 \cdot 115} = \sqrt{2300} \approx 47.96 \] When rounded to the nearest tenth, the car was traveling at approximately **48.0 miles per hour**. Ever wonder about the physics behind skid marks? They occur when a vehicle suddenly brakes, causing the tires to lose traction. The length of the skid marks depends on various factors including vehicle speed, road conditions, type of tires, and the force applied to the brake pedal. Understanding these can help prevent accidents and improve road safety! The formula used by police is based on physics principles that relate to kinetic energy and friction. It’s a nifty calculation that helps them quickly assess how fast a vehicle was moving. Law enforcement agencies often receive training on using these calculations effectively at accident scenes, ensuring they gather accurate data to support their investigations. Isn’t it fascinating how math helps keep our roads safer?