Kirill Z. answered • 08/23/13

Physics, math tutor with great knowledge and teaching skills

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=v^{2}/(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/s^{2} 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.