Accident reconstructionists are professionals that attempt to reconfigure the events leading up to a motor vehicle accident. These individuals use information about the scene like the weight of the car, the type of road, and the length of the skid marks to determine how fast a car was going before slamming on the brakes. They do this by manipulating some basic physics equations. When a car skids to a halt, the only force in the x direction is the force of friction, which is acting in the opposite direction of the motion of the car. To determine the magnitude of the frictional force (Eq1), the reconstructionist will have to find out the kinetic friction coefficient for the material which the road is made from and multiply that by the normal force of the car or mg.
Eq 1. FFR= μFN= μ*masscar*g (9.8m/s2)
We know that a car cruising will have a kinetic energy (eq2) while moving and will have 0 kinetic energy when it is stopped. This energy is lost from the system as it is converted into work done by nonconservative force, or in this case, work done by friction. Energy exits the system as heat and sound, as the evidenced by the skid marks left by tires and the loud screech the tires make when the brakes are slammed. Work done by nonconservative forces (Eq3) can be calculated as the force of friction multiplied by the distance the force is applied, in this case, the length of the tire marks.
Eq 2. KE= (½)mv2
Eq 3. WNC= WFR= FFR * dskid mark
There is no potential energy in the system so using conservation of energy KE = WNC. Now the reconstructionists can combine equations and figure the velocity before the driver slammed on the brakes (eq 4).
Eq 4. (½)mv2=FFR* d= μ*masscar*g * dv= sqrt(2μgd)