 Solution

At rest with all separations initially infinite, both initial kinetic and gravitational energies vanish, so the conserved total energy is zero. During an isolated collapse, $T+W=0$, rather than the equilibrium relation $2T+W=0$. Hence at the stated instantaneous gravitational potential energy,The rms collapse speed is $\sqrt{2}$ times the rms equilibrium speed for the same instantaneous $W$ and mass. For a perfectly radial cold infall this mean-square motion includes coherent inward streaming; it need not equal a local random velocity dispersion after subtracting that streaming. The quoted comparison follows the question's global mean-square convention.