Since the earth is slowing its rotation, and as far as I know, each day is 1 second longer every about 1.5 years, how long was an earth day near the formation of earth (4.5 billion years ago)?
I wouldn't assume to just do 4.5b/1.5 and subtract, because you would think the rate of change is changing itself, as seen here from wikimedia. It is a graphical representation of data from INTERNATIONAL EARTH ROTATION AND REFERENCE SYSTEMS SERVICE. They decide when its time for a leap second (the last one being on Jun 30, 2012) The data can be found here.
Best Answer
That figure is way off.
According to this Scientific American article, the Earth's rotation rate just after the collision that formed the Moon was about once every 6 hours. At that time, the Moon would have been about 25,000 kilometers away. The tidal effect of the Moon is the major reason the day has been lengthening, and the Moon's orbit has been widening.
The collision is believed to have taken place about 4.5 billion years ago, not long after the formation of the proto-Earth.
There are still some open questions about the impact hypothesis (see the linked Wikipedia article), so this is uncertain.
I strongly suspect that the impact would have erased any information about the Earth's rotation rate before the impact. (It might be possible to estimate the pre-collision rotation rate by modelling the initial formation of the Earth; I don't know whether there's been any research in this area.)