Final answer:
If the president and Vice President both die in a car accident, the Speaker of the House succeeds the presidency, as per the 25th Amendment and the Presidential Succession Act.
Step-by-step explanation:
Presidential Succession in the Event Both President and Vice President Are Incapacitated
If the president and Vice President are killed in a car accident, the next in line according to the Presidential Succession Act is the Speaker of the House. The 25th Amendment provides a clear line of succession after the Vice President. The historical instance of Vice President Lyndon B. Johnson becoming president after the assassination of President Kennedy illustrates the process of presidential succession in action. In the unlikely event the Speaker of the House is unable to assume the presidency, the President pro tempore of the Senate is the next in line, followed by members of the Cabinet in the order of their department's creation.