## Velocity/position from variable input force

I am looking for some help on calculating theoretical velocity and position of an object subjected to a variable input force. The situation is as follows:

weight of piston 14 lbs
force on piston 4150, (500 psi on 8.3 sq in)
stroke is just under 6 inches

The piston is in a 3.25 in bore, which translates into about 8.3 sq in. There is 500 psi on the piston when it is released. The amount of air at release is about 32 cu inches and as the piston moves forward the pressure drops due to the increase of 8.3 cu inches in volume for every inch of travel, which in turn results in a theoretically linear drop force on the piston.

Ignoring friction for now, (despite being able to estimate static and low velocity friction on the seals, at high velocities the hydrodynamic planning of lubricated seals gets a bit tough to estimate), what are the equations for calculating velocity and position of the piston over its 6 inch stroke?

Thanks for all of the help. RGA

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 Tags acceleration, piston velocity, variable force