Question

Police and private investigators often use the laws of mathematics to determine the circumstances behind incidents. One formula that is often used in car accident reconstruction is

S is equal to the square root of 21d

The formula says that S equals the square root of 21d.
The variables are defined as follows:

S= the car’s speed (in miles per hour)
d= the length of the skid mark (in feet)
Since police have the use of calculators in the real world, you are allowed to use a calculator in this lab to help you in determining the value of some radical expressions.
If a car is traveling at 60 mph and the driver applies the brakes in an emergency situation, how much distance is required before the driver comes to a complete stop? Round your answer to the nearest foot.

Answer 1

"how much distance is required before the driver comes to a complete stop? "

once the driver steps on the brakes, the skid marks on the pavement will start as well, therefore is really just asking, how long is the skid mark, namely what is "d".


`\bf S=√(21d)\qquad \boxed{S=60}\qquad 60=√(21d)\implies 60^2=21d \\\\\\ \cfrac{60^2}{21}=d\implies \cfrac{3600}{21}=d\implies \cfrac{1200}{7}=d\implies 171.42857\approx d`

other factors that can affect it will be, wind speed and wind direction, because the wind is acting on the car, atmospheric pressure as well, angle of the road, is not so easy to stop going downhill on a step hill, as opposed to a flat road. Other factors could be brake types, brake wear and tear, amount of weight in the car, if there are 5 sumo wrestlers in the car is not so easy to stop quickly.