In 2258, the Newton was docked at Starbase 1 at the time Vulcan came under attack by Nero. Several graduates of Starfleet Academy were assigned to this ship in the scramble to get a fleet to Vulcan. Upon its arrival at Vulcan, the Newton was immediately destroyed by the Narada in the Battle of Vulcan, along with a number of other starships. (Star Trek)
The Newton was briefly seen, however not specifically identified, when the shuttlecraft Gilliam flew over the spacedock to the USS Enterprise, and later in front of the Enterprise moments before warping to Vulcan. The registry number is the year in which Sir Isaac Newton died.
In the script of Star Trek, the Newton was assigned as the posting of Cadets Blake and Leifer for the Battle of Vulcan. Another line in the script, to be used as background chatter, had a cadet arguing that the Newton was not an antique but a classic, and that he or she would prefer it over the Enterprise.