__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.