Airworthiness Certificate
The airworthiness certificate is issued to certify the airplane has been found to be in an airworthy condition. It must be displayed on the aircraft so that it is legible to the passengers and crew. The airworthiness certificate remains valid so long as the airplane is maintained in accordance with the Federal Aviation Regulations.
Registration Certificate
The registration certificate must be carried on the aircraft as well. It details the registration information for the aircraft, and expires at the date shown on the certificate. This date is three years after the certificate's previous expiration date. Also, there are occurrences in which the registration will be invalidated, even if it has not expired. For example, if the airplane is sold, the certificate holder loses US citizenship, or if the aircraft were to be destroyed, scrapped, or registered in a foreign country.
Operating Limitations
The operating limitations of the aircraft, such as maximum speeds, fuel grade limitations, maximum oil temperature, etc., must be carried on the airplane. These limitations may be placed in the airplane as placards, or contained in an approved aircraft flight manual. Often times, the manufacturer uses a combination of placards and the limitations section of the approved flight manual.
Some aircraft do not have a flight manual (see FAR 21.5). However, if a manual exists for the aircraft, it must be carried on the aircraft.
The placards on the airplane must be legible. If the airplane's placards are excessively worn or damaged, they will need to be replaced before operating the airplane.
Instruments themselves also contain a lot of information about the operating limitations of the airplane, in the form of instrument markings. For example, the airspeed indicator and engine instruments contain colored arcs and lines to indicate a number of limitations.
§ 91.203 Civil aircraft: Certifications required.
§ 91.9 Civil aircraft flight manual, marking, and placard requirements.