Calculate Jerk

Calculating jerk from initial acceleration, final acceleration, and time. Jerk, also known as jolt, is the change in acceleration over time, essentially an acceleration of the acceleration.

jerk = ( end acceleration - start acceleration ) / time
j = ( a_e - a₀ ) / t

For example, if you accelerate from 0 to 5 m/s² within 8 seconds, the jerk will be 0.625 m/s³. This is a gentle start, a jerk of up to 2 is considered as such. Above about 5 m/s³, the jerk is perceived as unpleasant.

The word jerk is commonly used colloquially and is one of the probably not so rare cases where everyday language means the same thing as physics. A jerk is more than just a strong acceleration that continuously presses you into your seat, for example, in a car or airplane. The jerk is usually brief but intense. There is also a negative jerk, but like negative acceleration, this is usually referred to as braking.
A jerk always occurs when something transitions from a state of rest to movement, because at rest, both speed and acceleration are zero. However, during a very gentle start, this jerk is unnoticeable. The jerk is a relevant value in elevators, where it is often kept as small as reasonably possible.

Mathematically, jerk is the third derivative of distance over time. The first derivative of distance over time is velocity, because at constant velocity, the distance traveled increases linearly. The second derivative of distance over time is acceleration (see acceleration over time and acceleration over distance). At constant acceleration, velocity increases linearly. At constant jerk, acceleration would increase linearly, which in practice is only possible for a short period of time.