How short is "fairly short"? also when you say body you don't mean a person do you? it would be unwise to try to accelrate an untrained person much more that a very few "g".
1 g ia about 32f/s^2 so if you accelerated at 1 g you would reach your target speed in just under 1 second using 200lbf, if your air pressure was 100 PSI (a fairly common pressure for compressed air) you would need 2 square inches of effective piston area, just over 1.5 inches in diameter, the only problem is it would have to be about 15 feet long, probably not "fairly short". Also this assumes horisontal motion, if you try to go up you'd need 200lbf just to match gravity, so 400lbf and a 2-1/4 to 2-1/2" diameter cylinder. Lets try 10g, 1.5ft stroke is a little more reasonable, you'd need 2000lbf again at 100PSi that is 20 in^2 , about a 5 inch diameter cylinder. Note that you will have to rather large piping and valves and have a sizable air reservoir in close proximity to the cylinder..
1.5ft might still be a bit long, so lets try try for half of that at 20g, 4000lbf force (40 in^2, about a 7in diameter piston, but 8" might be easier to get, not that a cylinder that diameter is likely to be an off the shelf item anyway. The problem in this case, while the stroke is less than a foot, you have less that 50 milliseconds to fill the cylinder, a rather challenging task.
Looking at it from another direction, 4" diameter cilinders are about the maximum that are redily avaliable from stock from many vendors. 4" dia at 100PSI gives about 1250 lbf, I'll round that to 1000 to make some allowance for losses and to simplify later steps.
1000lbf will acclerate a 200lb at 5g. geting you to your target speed in about 0.2 seconds and about 3 feet. Oops, while 4" diameter cylinder in some lenghts would be "off the shell" a 36" stroke one will probably be a special again, but you'd need a special extral large fill port so I guess you'll need a coustom cylinder no matter what you do. If you try for vertical withthe 4" cylinder your net accelration will be 4g, (so the strolke will have to be around 3.5ft) 4 g is perhaps not too dangerous, I think some roller coasters get that high.
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