Final velocity squared = initial velocity squared + 2 * acceleration * distance
It would fall a distance of one yard (let's say, 1 meter)
Since the initial velocity is 0 , final velocity = square root of (2 * accel * dist) = sqrt(2 * accel * 1meter) = sqrt (2*acceleration)
= sqrt(2) * sqrt(acceleration)
Newton's law of gravitation: Force due to gravity = Universal gravitational constant * mass of object A * mass of object B, divided by the distances between their centers of mass (assuming a spherical spoon)
Since this would provide the net force acting on the spoon, and force = mass times acceleration, the acceleration is equal to the force divided by the mass. Thus, the mass of the spoon is irrelevant since the mass of the spoon cancels out. (i.e., if you drop a copper ball and a lead ball from the same height, they hit the ground at the same time).
So, the acceleration = universal gravitational constant, times the mass, divided by the distance squared.
Substituting, that gives a final velocity of sqrt(2) times sqrt(G * mass of neutron star) divided by r (the sqrt of r² is just r)
The mass of a typical neutron star is approximately 1.4 to 2 solar masses; let's go with 2. So, replacing mass with 2solar masses reduces to
final velocity = 2*sqrt(G * solar mass)/r
The typical diameter of a neutron star is around 12 kilometers, so, the distance is around 6000 kilometers. (6000 + 1 if the 12km is precise) The solar mass is just shy of 2 x 10^30 kg, and the universal gravitational constant is 6.67 x 10^-11 Nm²/kg²... let's see...
3849 meters per second. (multiply by 2.2)
I got roughly 8500 miles per hour.
edit: miles per second, not miles per hour. Derp!