massless piston. The piston is supported by a linear (Hookean) spring.
The question is unphysical.
The acceleration is a = F/m which will be infinite for almost
any net force F. For the net force to be zero would require a
balance of the contributing force, and the statement of the problem
does not suggest that such a balance has occurred.
A massless piston is only slightly different from no piston at all.
So the situation should be analyzed almost the same way you would
analyze free expansion of the gas. The piston will be driven by
collisions with the fastest molecules in the sample of gas. In the
hydrodynamic limit (i.e. lots of molecules), there will be "some"
molecules with arbitrarily high velocity, so the piston will have
unbounded speed as well as unbounded acceleration.
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Even taking the question more seriously than it deserves, even if you
were to hypothesize some sort of equilibrium between the /average/
pressure and the /average/ force exerted by the spring+piston, the
question would still be unphysical.
By equipartition, the piston would undergo Brownian fluctuations in
accordance with .5 m v^2 = kT and in the limit as the mass goes
to zero, the RMS velocity would be infinite.