Slide to Stop Formula

When there is a major motor vehicle accident, an accident reconstructionist is often called in. One of the most critical pieces of information needed is the velocity of each vehicle. This is used to determine if the speed limit was broken and if speed was a contributing factor to the accident. In a fatality, the speed can cause a driver to be prosecuted for either manslaughter( a felony), negligent homicide(a misdemeanor), or not criminally charged at all. The main formula that officers use is the 'slide-to-stop formula' v = 15.9 (d u n)^1/2 . d is the length of the skid marks in (m), and u is the coefficient of friction of the roadway and the tire, n is the % of tires that braked, and v is the minimum initial speed needed to travel the skidmark distance. An automobile must have its brakes fully locked to leave skidmarks. Therefore, the minimum traveling speed before slamming on the brakes can be found. So how did they get this formula anyway? Simple physics.

Work = kinetic Energy

Here Force is the retarding force of the road on the car.

W = F d, u = Force / mg; F = u m g

W = u m g d

KE = 1/2 m v^2

u m g d = (m v^2) /2

v^2 = 2 u g d v = (2 u g d)^1/2 = 4.42( u d)^1/2 (in m/s)

= 15.9( u d)^1/2 (in km/hr)

A police officer is only interested in a minimum speed for legal purposes. As well, to use momentum in court, the officer must establish the path of approach and departure for each vehicle, the approximate weight and load of each vehicle, and the speed of the vehicles after impact. With all of this, the acceptance/rejection rate in court in only about 50/50.

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