In Newtonian mechanics, what derivative of acceleration is called jerk?

In Newtonian mechanics, jerk is the time derivative of acceleration.

Written mathematically, jerk is j = da/dt. It measures how quickly acceleration changes, not how quickly an object changes position or velocity. Because acceleration has SI units of metres per second squared, jerk has units of metres per second cubed, commonly written m/s³.

Jerk is also the second time derivative of velocity and the third time derivative of position. A car moving with constant acceleration has zero jerk, while a sudden change from braking to no braking produces a large jerk even if the acceleration itself is not especially large.

The concept matters in vehicle design, elevators, railways and spacecraft because abrupt acceleration changes can be uncomfortable or damaging. Engineers therefore shape motion so acceleration changes more gradually. The next named derivative is snap, or jounce, the time derivative of jerk; higher derivatives are sometimes called crackle and pop.