Jerk (physics)

In physics, jerk or jolt is the rate at which an object's acceleration changes with respect to time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s3 (SI units) or standard gravities per second (g0/s). As a vector, jerk j can be expressed as the first time derivative of acceleration, second time derivative of velocity, and third time derivative of position: Where: a is acceleration v is velocity r is position t is time Third-order differential equations of the form are sometimes called jerk equations. When converted to an equivalent system of three ordinary first-order non-linear differential equations, jerk equations are the minimal setting for solutions showing chaotic behaviour. This condition generates mathematical interest in jerk systems. Systems involving fourth-order derivatives or higher are accordingly called hyperjerk systems. g-force#Human toleranceHuman tolerance of g-force and motion simulator#HumanPhysiologyResponseToMotionHow human physiology processes and responds to motion Human body position is controlled by balancing the forces of antagonistic muscles. In balancing a given force, such as holding up a weight, the postcentral gyrus establishes a control loop to achieve the desired equilibrium. If the force changes too quickly, the muscles cannot relax or tense fast enough and overshoot in either direction, causing a temporary loss of control. The reaction time for responding to changes in force depends on physiological limitations and the attention level of the brain: an expected change will be stabilized faster than a sudden decrease or increase of load. To avoid vehicle passengers losing control over body motion and getting injured, it is necessary to limit the exposure to both the maximum force (acceleration) and maximum jerk, since time is needed to adjust muscle tension and adapt to even limited stress changes. Sudden changes in acceleration can cause injuries such as whiplash.