For when one would come across a constant jerk - how about the usage case of putting a stopped vehicle into motion? You gradually push the accelerator or throt

For when one would come across a constant jerk - how about the usage case of putting a stopped vehicle into motion? You gradually push the accelerator or throttle from zero to maximum at a constant pace - that's increasing the acceleration linearly (ignoring friction/drag), thus constant jerk, which the occupants will perceive as a smooth start. This probably doesn't often get solved numerically, but it's something you do instinctively do.