Final answer:
John F. Kennedy's inaugural address excerpt primarily relies on an appeal to pathos, seeking to inspire and motivate the audience by invoking shared emotions and a sense of long-term communal effort.
Step-by-step explanation:
The excerpt from John F. Kennedy's inaugural address mainly relies on an appeal to pathos. Kennedy is reaching out to the emotions and shared feelings of his audience, invoking a sense of beginning together a journey that might not be completed even in their lifetimes. This emotive approach is designed to inspire and motivate the audience to commit to long-term efforts, recognizing that the fruition of their labors may not be seen immediately but is nonetheless worth undertaking.
While ethos and logos are also important rhetorical strategies and are often used in conjunction, in this passage from Kennedy's speech, the primary appeal is to the audience's emotions — their hopes and aspirations for what they can begin together, implying a shared responsibility and mission that transcends their individual lifetimes.