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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