Concept# Jerk (physics)

Summary

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).
Expressions
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:
\mathbf j(t) = \frac{\mathrm{d} \mathbf a(t)}{\mathrm{d}t} = \frac{\mathrm{d}^2 \mathbf v(t)}{\mathrm{d}t^2} = \frac{\mathrm{d}^3 \mathbf r(t)}{\mathrm{d}t^3}
Where:
*a is acceleration
*v is velocity
*r is position
*t is time
Third-order differential equations of the form
J\left(\overset{\mathbf{...}}{x}, \ddot{x}, \dot{x}, x\right) = 0
are sometimes called jerk equations. When converted to an equivalent system of three ordinary fi

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