Skid Marks and Accident Reconstruction and Investigation - The Skid Mark Equation

In a college algebra course, we may learn that "the stopping distance of a car is directly proportional to the square of its speed." The formula for this is:

D = k●V²  where D is the stopping distance in feet, V is the speed in miles per hour, and k is a constant that depends on the frictional force of the pavement on the wheels of that particular vehicle. To accurately use this formula, one must:

• Experimentally determine the constant k for the particular vehicle in question driven on the same pavement, in the same driving conditions. Drive at a known speed V. Brake suddenly. Measure the skid mark D.   Use this data to solve for k.  The algebraic solution of D = k●V² for variable k is
  
• Measure the skid mark D for a different speed.
• Substitute the value of D into the equation
  

My Own Skid-Mark Experiment (Watch The Video!)
My brother-in-law (a former law enforcement officer), myself, and my sons decided to try out this formula by conducting our own experiment. As the test driver, I locked up the brakes on my 2003 Kia at a speed of 30 MPH several times to get an average skid mark of 33 ft, 4" or 33.33ft. Plugging into
 
this results in a value of k = 33.33/(30²) = 0.037

So, for this particular vehicle on this particular pavement, D = 0.037●V²

I then increased the speed to about 35 MPH and locked the brakes. Surprisingly, the extra 5MPH resulted in a skid mark of 50ft!  According to our formula
.
Plugging D=50, we get V = 36.8 MPH.  Not Bad!

I have found this formula referenced on the internet, and my brother-in-law Retired Sheriff's Deputy Murray  also used this formula and other mathematics while on the job.

NOTE: When measuring the skid mark, you need to measure from where the mark first begins, however faint. This was pointed out to me by retired Deputy Murray as we were conducting this experiment.

Factors To Consider
In the tests shown on the video, the skid mark equation worked quite well because we obtained the constant k using the actual vehicle on the actual pavement. Other factors to take into account include:

• Is the pavement wet or slippery?  Investigators account for this by actually doing a pavement test at the scene.
• What are the condition of tires? Again, investigators account for this and adjust calculations.
• Is there an incline to the pavement up or down?  If so, this must be recorded and the calculation must be adjusted.
• Did the car impact some other car or object while skidding? If so, a modified formula must be used. See this story.