= Solution
Take the initial internal <pressure> as negligible and the external <atmospheric pressure> as $p_0=1.01325\times10^5\,\mathrm{Pa}$. The window has frontal <area> $A=\pi(0.400\,\mathrm m)^2=0.50265\,\mathrm{m^2}$. Before appreciable air has entered, its inward pressure <force> is approximately $p_0A=5.09\times10^4\,\mathrm N$. <Newton's second law> therefore gives the initial collective inward <acceleration>
$$
\boxed{a_0\simeq\frac{p_0A}{M}=4.63\times10^2\,\mathrm{m\,s^{-2}}\simeq47\,g.}
$$
Here $M=110\,\mathrm{kg}$ and $g\simeq9.81\,\mathrm{m\,s^{-2}}$. Neglect gravity in this much larger pressure-driven <acceleration>, together with supports and elastic stresses once the glass has broken. The given thickness $d=0.080\,\mathrm m$ implies a plausible average glass <mass density> $M/(Ad)\simeq2.74\times10^3\,\mathrm{kg\,m^{-3}}$. Equivalently, a fragment retaining the original thickness has <acceleration> $p_0/(\rho_gd)$, independent of its frontal <area> while it experiences the full pressure difference.
For a <vacuum-window implosion energy estimate>, the ideal pressure-work scale for filling vessel <volume> $V=1.5\,\mathrm{m^3}$ is $W\simeq p_0V$. Assigning all that <pressure-volume work> to the glass's <kinetic energy> gives
$$
\frac12Mv_{\mathrm{est}}^2\simeq p_0V,
\qquad
\boxed{v_{\mathrm{est}}\simeq\sqrt{\frac{2p_0V}{M}}\simeq5.26\times10^1\,\mathrm{m\,s^{-1}}.}
$$
The same result follows from retaining <acceleration> $a_0$ over an effective swept distance $V/A\simeq2.98\,\mathrm m$, so that $v_{\mathrm{est}}^2=2a_0V/A$. This is an ideal upper energy-budget estimate for the common <speed>, or <mass>-weighted <root mean square> <speed>, of all the glass. It assumes an atmospheric reservoir maintains the driving pressure and that the whole vessel's pressure-work budget can accelerate the glass. In practice, air motion, fragmentation, heating and collisions share that <energy>, the pressure difference falls, and fragments may hit the vessel after a much shorter path. The unspecified vessel shape and fragment trajectories prevent a unique actual maximum <speed>; concentrating <energy> into one small fragment also prevents interpreting this collective estimate as a strict bound on every individual fragment.
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