Why don't we consider jerk in physics classes?

Question

When I got more into physics, I started asking myself if just like acceleration represents the growth of speed, something else could also represent the growth of acceleration itself. And it came that is exists and is called _jerk_. Before I thought about this, I thought that acceleration was the highest derivative that made sense on physics. My question is, why can we perform accurate calculations without account for _jerk_? I never needed it in a single physics class! I've also read that it is seldom used. Also, while position, speed and acceleration seem familiar to me due to everyday experience, why doesn't _jerk_ seem familiar to me? I never tell someone when driving a car "you're jerking too much", whereas I could say "you are accelerating too much". Is it that jerk has little influence because it is almost constant? Even if it is not, what about higher order derivatives? Why don't derivatives higher than acceleration have much influence on calculations? We perform a lot of reasoning in everyday life without resorting to it!

Answer 1

In Classical Mechanics, the motion of physical objects is completely specified by Newton’s 2nd Law, which relates force to acceleration. Force is almost always a function of position alone, and acceleration is the 2nd derivative of position with respect to time. The resulting equations of motion are necessarily 2nd order differential equations in position as a function of time. So, to solve for an object’s motion, we only need to consider two state variables, position and velocity, along with their time rates of change, velocity and acceleration. The notion of “jerk” never shows up, and is thus unnecessary in describing or predicting motion.

That does not mean that jerk is not interesting or even useful. For example, if you are a passenger in a moving vehicle — e.g. automobile, aircraft, boat, or rocket ship — you may be very interested in jerk. Specifically, you may very well prefer to minimize or even eliminate jerk as much as possible, as unexpected changes in acceleration can create serious problems, especially if you are not strapped in.

Answer 2

In most fundamental classes, we generally deal with acceleration which is constant (or averaged over time). To even have jerk, we would need an acceleration which depends on time. You can do a lot of physics without worrying about it, though it definitely comes up in engineering design (for example, any fundamental physics problem describing direct transition of a roller coaster car from a straight track to a circular loop would run into significant problems with jerk).

In terms of the real-world experience of these effects, I describe it by talking about imagining driving in a car on a long, straight, flat road with no bumps. If you are in such a situation, and close your eyes (and ignore any road noise or noise from your car), it can fell like you're just sitting in a chair at home, with no particular stresses on you (except gravity and the normal force, which are always there in cases like this). This is predicted by Newton's laws of motion, which make no distinction between being at rest or being in motion at constant velocity (constant in magnitude AND direction).

Now imagine the driver (who I presume is not you; otherwise, don't close your eyes in the previous part! :D ) evenly applies the brake to slow down. You will feel a pull (the actual pull is backward, though inertia may make it seem you are leaning forward). This sort of pull (or push) is how we generally physically experience acceleration.

By the way, the meaning of the word acceleration in physics is rather different from everyday usage. In common use, it often means "speeding up." But in physics, it is specifically "change in velocity over time," and there is acceleration both in "speeding up" and "slowing down." We can talk about that in a little more detail, if you like.

Now, imagine the driver is braking evenly, and then suddenly mashes their foot onto the pedal (perhaps to avoid some suddenly apparent hazard). You may have experienced this sort of thing before. You will probably feel a "jerk" in you seat. This is most likely the source of the name jerk, and results from the fact that the acceleration is changing with time over that interval. We may not use "jerk" commonly in situations like this, as we use acceleration for changing speeds, but that is what it is.