In physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, jerk, also known as jolt (especially in British English

British English

British English, or English , is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere...

), surge and lurch, is the rate of change of acceleration

Acceleration

In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

; that is, the derivative

Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

 of acceleration with respect to time, the second derivative

Second derivative

In calculus, the second derivative of a function ƒ is the derivative of the derivative of ƒ. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of a vehicle with respect to time is...

 of velocity

Velocity

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, or the third derivative of position. Jerk is defined by any of the following equivalent expressions:

where is acceleration, is velocity, is position is time.

Jerk is a vector, and there is no generally used term to describe its scalar magnitude (e.g., "speed" as the scalar magnitude for velocity).

The units

SI base unit

The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

 of jerk are metre

Metre

The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s per second

Second

The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

 cubed (metres per second per second per second, m/s³ or m·s⁻³).