Updated by Stephanie Gragert, 1998.
Original by Philip Gibbs, 1996.
The first derivative ofdisplacementx with respect to time isvelocityv, and thesecond derivative isaccelerationa. Less well known is that the third derivative of displacement (and sothe rate of increase of acceleration), is technically known asjerkj. Jerk is a vector, but may also beused loosely as a scalar quantity because there is no separate term for the magnitude of jerk analogous tospeed for magnitudeof velocity.
In the UK,jolt has sometimes been used instead of jerk, and is equally acceptable.
Many other terms have appeared in individual cases for the third derivative, including pulse, impulse, bounce,surge, shock and super acceleration. These are generally less appropriate than jerk and jolt, either becausethey are used in engineering to mean other things, or because the common English use of the word does not fit thetechnical definition so well. For example, impulse is more commonly used in physics to mean the increase ofmomentum imparted by a force of limited duration [Belanger 1847], and surge is used by electricians to mean somethinglike an increasing current or voltage. The terms jerk and jolt are therefore preferred for rate of increase ofacceleration. Jerk appears to be the more common of the two. It is also recognised in internationalstandards:
In ISO 2041 (1990), Vibration and shock – Vocabulary, page 2:
"1.5 jerk: A vector that specifies the time-derivative of acceleration."
Note that the symbolj for jerk is not in the standard and is probably only one of many symbols used.
As its name suggests, jerk is important when evaluating the destructive effect of motion on a mechanism, or thediscomfort caused to passengers in a vehicle. The movement of delicate instruments needs to be kept withinspecified limits of both acceleration and jerk to avoid damage. Engineers who design a train aretypically required to keep the jerk less than 2 metres per second cubed for passenger comfort. Theaerospace industry even has ajerkmeter: an instrument for measuring jerk.
In the case of the Hubble space telescope, the engineers are said to have gone as far as specifying limits on the magnitude of thefourth derivative of displacement. No name for this fourth derivative—the rate of increase of jerk—is univerallyaccepted. The termjounce has been used, but has the drawback of using the same initial letter as jerk. Higherderivatives do not yet have names because they seldom appear in physics.