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From Wikipedia:

In physics, jerk is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, and as such the second derivative of velocity, or the third time derivative of position.

Often (always?) engines will be allowed to reach full thrust before clamps are released and the rocket allowed to rise. See for example this answer. With thrust > weight and instantaneous de-clamping, a perfectly rigid rocket would experience infinite jerk as the acceleration would be a step function.

In reality, rockets are not perfectly rigid, and the seats in which astronauts sit during launch will have some amount of shock absorbing activity.

Are there any reports of the amount of jerk experienced by astronauts, or any safety limits on it?

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The NASA Commercial Crew requirements document discusses this and other “Crew Acceleration and Vibration Limitation(s)” starting on page 155.

The jerk limitation is 500 g/sec during “non-impact” flight. That’s an interesting exclusion...

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  • $\begingroup$ I've had some time now to review the document, thanks for the link! "impact acceleration" is covered in section 4.3.10.3.1 B. $\endgroup$ – uhoh May 1 '18 at 2:11

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