jakiri is correct, one can and will never determine how long that instant is. The value relies entirely on the sensitivity of the measuring device. It is the same concept as a board which measures 1.3 meters. That board, most likely does not have a length of 1.3 meters. Instead it has 1.345629876...ect meters. It all depends on how precise your measurements are.
Back to the case with the instant in time, a ball thrown up in the air has no definite begining and end to the time that it is moving. Just like the board, the ball could be moving at .0001nm per second, to small to be measured by anything that we have today, but it is still moving. The ball has a velocity of zero for as long as sensitive you measuring device is to when it starts and stops.
Therefore, to answer you question, the instant is, as Jakiri said, 1/infinity seconds. It cannot be measured ever.