What is the velocity and acceleration of a free falling object on the Moon?

Since the moon has no atmosphere, there is no air resistance.  The position function for objects on the moon is:

s(t) = -0.81t^2 + 2, where s(t) is the height in meters and t is the time in seconds.

You can then use derivatives to find the velocity and acceleration formulas.  Using the power rule, the above formula becomes:
s'(t) = -1.62t, the velocity function

Further refining shows the acceleration function to be s"(t)  -1.62.

With no resistance, acceleration is constant.  No matter which interval of the fall, acceleration is -1.62 meters / second / second.

For velocity, plug and solve:
s'(3) = -1.62(3) = -4.86 meters / second / second