You can assume that water molecules fluctuate around the equilibrium distance given by the LJ potential. If we have a harmonic approximation around this point with

U = 1/2 K (r - r_eq) ^ 2

we come up with the oscillatory solution

r = r_eq + A sin (w t)

with w = sqrt (K / m). The velocity and accelerations would be:

v = A w cos (wt)

a = -A w ^ 2 sin (wt)

Now, this way, the actual "mean" velocity and acceleration become zero. If we consider the root mean square values, we have:

v_rms = A w / sqrt (2)

a_rms = A w ^ 2 / sqrt (2) = v_rms * w

We can get an approximation of v_rms from Maxwell-Boltzmann distribution:

v_rms = sqrt (3 kT / m)

For the 12-6 Lennard-Jones, the spring constant around the equilibrium distance is:

K = [72 / 2 ^ (1/3)] * eps / sig ^ 2

For numerical values, I have used SPC water model with

sig = 0.3166 nm

eps = 0.650 kJ / mol

This will result in

a_rms = 2.79 x 10 ^ 15 m / s^2

I think this is straightforward enough and you can check the results for yourself.

Thanks for answer.

You are quite welcome!