A rock dropped on the moon will increase its speed from 0 its starting speed to 8.15 in about 5 seconds If you were standing on the moon measuring the rock's motion what would you measure?

That works out at an acceleration of 1.63 m/s2

(Presumably you meant 8.15 meters per second.)

You would measure how far the rock dropped in 5 seconds. Then you could work out the final speed (or acceleration) from the "equations of motion".