Your max speed spec limits response to >10 ms, neglecting acceleration.
Why do you care about peak speed? Just curious.
It probably doesn't matter; getting response under 50ms is difficult when any mechanical part or large force is involved.
Not impossible; see "Lucas Helenoid" for a historical reference that didn't quite make it.
Solenoids are capable of large forces, but only for a short portion of their stroke, and their inductance limits the rise time of current (and force), so you may need a driver circuit that whacks it with high voltage, then applies a much lower voltage to keep it in place. Such circuits have been done, but development can be expensive because they tend to turn to smoke when things don't go according to plan.
I once knew a PhD who analyzed a solenoid and its mechanical environment and its driver circuit, all together in some kind of math model (before anybody had computers) in order to predict its performance, and then changed parameters in order to optimize the solenoid and everything else, in order to make the solenoid and such start a magnetic tape in response to an audio signal, and record the signal without a noticeable gap at the beginning of the recording. I don't think he ever got there until he started digitizing the audio and putting it through a long wide shift register that sort of duplicated a much older mechanical device that recorded the audio continuously on a continuously rotating ferrite drum and read it off the drum after half a rotation.
I can't do most of that analysis, and probably wouldn't bother trying anyway.
I'd start by ordering an assortment of solenoids and measuring what they can do in your apparatus, just to see how far out of the solution space you actually are.
Mike Halloran
Pembroke Pines, FL, USA