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fifth derivative of the displacement; fourth derivative of velocity

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In the physics field of kinematics, the fourth, fifth and sixth derivatives of position are generalizations of velocity and acceleration. They are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. These higher-order derivatives are less common than the first three; thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics.

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