President Carter yesterday signed into law a bill that authorizes an additional $750 million over the next five years for completion of a high-speed passenger rail corridor between Washington and Boston.

The rail law also allows the continuation of freight service by other railroads along the lines of the bankrupt Rock Island Railroad, and contains federal spending provisions designed to soften the impact of the bankruptcy on freight service in the Midwest and on the railroad's employes.

In a signing ceremony in the White House Rose Garden, Carter said the multi-purpose legislation would improve riding conditions for Amtrak riders and add to their numbers, as well as aid the revitalization of central cities in the Northeast with improved rail service, new jobs, less dependency on the automobile, and reduced air pollution.

"That's a lot of benefits from one bill," the president said. He said he was particularly optimistic about the "very bright" future for rail transportation in the United States. "Americans sometimes forget that trains are the transportation of the future, not the past," he said.

The ceremony got off to a late start when Carter waited a few minutes for New Jersey Gov. Brendan Byrne, who didn't arrive until half-way through the ceremony. "In the future, with a better Northeast rail corridor, he'll get here in time," Carter quipped.

The $750 million in new funding for modernization of train travel on the Northeast corridor raises the total cost of the project to $2.5 billion. Authorized by Congress in 1976 and originally scheduled for completion by February 1981, the project's goal is to achieve dependable Amtrak service along the 456-mile corridor at speeds of up to 120 miles an hour.

But it was made clear this was the project's last authorization.

"In this legislation, we tell them, 'this is the end of the line and we ain't going any farther,'" Sen. Howard W. Cannon (D-Nev.), chairman of the Senate Commerce Committee, explained before the ceremony.

He also said Amtrak has been told to recover all its operating costs out of the fare box by 1987. It now recovers about half.

Of the new funding, $37.2 million is earmarked for improvements in the Baltimore tunnel along with some experimental diversion of freight traffic from the corridor in an effort to eliminate congestion and meet the passenger train speed objectives.

Another $38 million is authorized for the study of additional high speed rail corridors around the country, by both the secretary of Transportation and Amtrak.

The signing came just in time to avert disruptions of freight rail service in parts of the Midwest. The authority used by the Interstate Commerce Commission to allow 16 freight railroads to operate along portions of the Rock Island would have run out tonight at midnight without the new authority contained in the legislation.

Acting immediately, the ICC yesterday afternoon told the 16 railroads to continue operating on a temporary basis until agreements for them to purchase the lines can be completed.