In physics terms...
Jerk is basically the rate of acceleration.
- When jerk is at a constant value, the acceleration is changing at a constant rate, thus the velocity is changing quadratically.
- When jerk is increasing at a constant rate, acceleration is increasing quadratically. The jerk also decreases at a constant rate as the acceleration decreases quadratically.
- When jerk increases quadratically, the acceleration increases cubically, making the velocity increase to the fourth degree. The same situation occurs when they are all decreasing.
- When jerk exponentially decays, the acceleration decreases at a constant rate, which means the velocity would be decreasing quadratically.
Jerk is what is mainly describes as a sudden change in acceleration, such that if the acceleration is at a constant value most of the time, and it increases the value within a short period of time and goes back to constant, the jerk would be a little bump if this was shown on a graph. This is what causes motion sickness due to the unexpectancy of change in acceleration.
In math terms...
Jerk is the derivative of acceleration, as acceleration is the derivative of velocity, etc. This makes jerk the second derivative of velocity.
If the function of velocity is:
(Let t = time in seconds, and f(t) be the distance, in meters.)
v = f(t) = 8t2
...where the
domain of t is [
0,
∞)
a = f'(t) = 16t
j = f''(t) = 16
∴ jerk is constantly at 16 when the velocity is at 8t2.
All in all, jerk, in this context, is a form of movement, not to get mixed up with a passenger who would furtively shift the car to reverse in the middle of heavy traffic, or someone who would grind sleeping pills into your cereal on the morning of SAT's. That would be of slightly different context.