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If you had to pass through turbulent air, and your only goal was to give the smoothest ride possible to your passengers, would you push that throttle or would you reduce the throttle, or would it be the same either way?

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The ride is better slower, for the same reason that speed bumps work for cars: the more rapidly you transition from an updraft to a downdraft to an updraft, the greater the felt change in acceleration, or "jerk". Or, put simply, the worse the ride.

The limit there is that you don't want to go too slow in turbulence for other non-ride-related reasons, such as wanting to keep a comfortable margin above low-speed buffet. Large aircraft will generally have a turbulence-penetration airspeed published, and that speed is typically somewhat slower than normal cruising speeds.

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    $\begingroup$ However at infinitesimal high speed the duration of the bump is infinitesimal small giving a smooth ride without long travel times :D $\endgroup$
    – U_flow
    Feb 27 at 14:31

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