The following article is taken from Letters, The Physics Teacher, October, 1988, p. 423.

What a jerk!

A friend who drives race cars as a hobby approached me recently with a question about a race he had recently driven on a wet track. Like many others that day, he had slid off the track onto the wet grass inside the oval. He and another driver had been discussing what happened when the car hit the grass. The sensation the drivers had was that they seemed to speed up when the car left the track surface and slid onto the grass, even though the car's brakes were on. The question I was asked was whether this is really what happened.

My friend is a chemist who works with floor wax (among other things) so he is familiar with coefficients of friction. He reasoned that the friction coefficient on the wet grass is less than that on the road surface. Therefore, the retarding force on the skidding tires is reduced. reducing the car's deceleration, causing the car to speed up. I pointed out that the car is constantly slowing down, even when it slides onto the grass. It never experiences a positive acceleration, so it can’t speed up.

I then realized that this is an example of an old kinematic quantity that I have never seen in a modern physics text. We are all familiar with the relationships between displacement, velocity, and acceleration. Much less well-known is the jerk, which is the rate of change of acceleration. (I would give a reference, except that I don't know of one!) What happened to the racer is that it underwent a positive jerk as it slid off the track onto the grass. What the driver felt was a sudden decrease in the pressure that his shoulder straps exerted on him. He interpreted that as a momentary "force" pushing him against the back of his seat, an experience that is normally associated with positive acceleration. But the car does not really go faster, it just does not slow down as rapidly.

I mentioned this to some colleagues at a recent meeting, and a lively discussion arose concerning other jerk-related effects. They may be more common than we realize. I would be interested in other examples that people can think of. I would also like to know if anyone can find a reference that defines "jerk.".

Stephen Luzader, University of Wisconsin-Parkside, Kenosha, WI 53141

Editor's Note

The use of the word jerk to mean da/dt (or d³s/dt³) is quite old even though it is seldom mentioned in introductory mechanics. This physical meaning follows directly from the definition: "to give a quick suddenly arrested push, pull, or twist to."¹ This definition indicates behavior for which (dF/dt) is not zero. Therefore, from F = Ma, we are considering situations where (da/dt) is not zero. About 35 years ago in a company training course, I remember one assignment was to "design a jerkmeter." The introduction to this problem explained that passenger comfort on public conveyances depends on any accelerations being either very small or maintained nearly constant. Passengers are then easily able to exert the constant force that will maintain them at rest relative to the conveyance. It is the non-zero (da/dt) that passengers cannot anticipate that results in their uncomfortable (and sometimes injurious!) position shifts within the vehicle.

1 . Websters Ninth New Collegiate Dictionary, Merriam Webster Inc., Publishers, Springfield, MA.