Beyond Acceleration

Jedimentat44 © Flickr, CC BY 2.0

My favourite subject in school this year is physics. Recently we completed a unit on Kinematics, and studied that velocity is the rate of change in position of an object, and acceleration is the rate of change in velocity of an object. The teacher did not mention anything past that and left it to our imaginations. I was so interested that there was such a thing as rate of change in acceleration, or acceleration/time, and that it was a calculable and applicable function. I asked my teacher about it, who said that she knew little about it. Naturally, I resorted to looking it up on the trusty web.

The rate of change in acceleration is called jerk. It is the third derivative of position. Jerk is calculated by dividing the change in acceleration of an object by time. On an acceleration/time graph, jerk is the slope in the straight line on that graph. On a velocity/time graph, jerk would look like a curved line. Jerk is a difficult concept to imagine. A way to think about it is to picture a driver of a car stepping halfway on the gas pedal for a second and then stepping fully on the gas pedal. The car starts out accelerating slower and then changes to accelerating faster.

The fourth derivative of position is called jounce. As you may have guessed already, jounce is the rate of change in jerk. It is calculated by dividing the change in jerk of object by time. On a jerk/time graph, jounce is the slope, and the line will be straight. On an acceleration time graph, jounce would look like a curved line. Jounce is almost impossible for us humans to imagine and is only rarely used in practical physics. It is more of a value that physicists play around with just for the sake of doing theoretical physics.

The next few derivatives are truly not applicable in practical and tangible physics and are considered a kind of “joke” in the physics world. Their names prove this. They are known as crackle, pop, lock and drop (in ascending order).

I enjoyed my adventure of discovering the names and uses of some of the higher derivatives of position after velocity. My teacher did not believe me when I told her about crackle, pop, lock, and drop, but was excited to hear that I was so invested on this topic!

 

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