In motion control, a common need is to move a system from one steady position to another (point-to-point motion). Following the fastest possible motion within an allowed maximum value for speed, acceleration, and jerk, will result in a third-order motion profile as illustrated in this image:

The motion profile consists of up to 7 segments defined by the following:

1. acceleration build-up, with maximum positive jerk
2. constant acceleration (zero jerk)
3. acceleration ramp-down, approaching the desired maximum velocity, with maximum negative jerk
4. constant speed (zero jerk, zero acceleration)
5. deceleration build-up, approaching the desired deceleration, with maximum negative jerk
6. constant deceleration (zero jerk)
7. deceleration ramp-down, approaching the desired position at zero velocity, with maximum positive jerk