Final answer:
The increase in Earth's day by 0.002 seconds per century indicates that the Earth's rotation is slowing down. It would take an infinite amount of time for Earth to come to rest.
Step-by-step explanation:
The increase in Earth's day by 0.002 seconds per century indicates that the Earth's rotation is slowing down. If this increase is constant, it would take an infinite amount of time for Earth to come to rest. This is because the gradual increase in Earth's day is due to the transfer of angular momentum from Earth's rotation to the Moon's orbit, which will continue as long as the Moon's orbit exists.