Equations Word Problem

Question

The formula can be used 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. If a car is involved in an accident and its skid marks measure 211.25 feet, at what estimated speed was the car traveling when it applied its brakes just prior to the accident?

Answer 1

When car brakes, its speed decreases due to the friction force. The friction force depends on the car's weight and the cohesion with the road (dry, wet, asphalt, concrete). The formula for the distance traveled upon braking is given by:

L=v²/(2*a), where a is the car's acceleration due to friction force. The acceleration (actually, deceleration, but it's not important here) is given by:

a=k*g, where g is the acceleration due to gravity (9.8 m/s² near the Earth's surface), k is the friction coefficient, describing how well the wheels stick to the road pavement. Unless you know k, your problem can't be solved. I looked it up, it is 0.5 to 0.8 for the rubber on dry asphalt. Let us take k=0.65 as the estimate. Then the velocity of the car can be found as follows:

v=√(2*L*k*g); You are given L=211.25 feet, so L=64.22 m; Then, upon substituting the numbers you will get the velocity in m/s. Convert it into mph (by multiplying by 2.25), and you are done.