foe alike, that the torch has been passed to a new generation of Americans-born in this century, tempered by war, disciplined by hard and bitter peace, proud of our ancient heritage, and unwilling to witness or permit the slow undoing of those human rights to which we are committed today at home and around the world.

Kennedy's emphasis on "war" and his vivid reference to "hard and bitter peace" should make the listener feel compassion, sorrow, and thankful for those who fought, died, and suffered for the rights and privileges that a number of Americans now enjoy.

This quote ends with:

[...] we shall pay any price, bear by burden, meet any hardship, support any friend, oppose any foe, in order to assure the survival and the success of liberty.

Here, Kennedy seems to pivot back to ethos, creating an us versus them equation. “We,” like those who came before us, are a part of that "ethos"—i.e. culture or spirit—of “liberty.” Like our “heirs,” according to Kennedy, we will use whatever means necessary to "assure" the “success” of that guiding principle.

John F. Kennedy appeals primarily to pathos in his inaugural speech, as quoted here. While the ethical or moralistic qualities of ethos enter as well, they largely serve to support Kennedy's emotional appeal rather than parallel it.

Kennedy effectively uses first-person plural to encourage the listener to identify with him and his message. He never says "I" in this passage, always "we." This is consistent with his earlier address to the listeners as "my fellow Americans." Kennedy implies that we are all in this together, that we share the same goals.

Similarly, the new president puts forward a kinship of age and vitality. He, too, was born in the 20th century, he was a veteran "tempered by war," and was disciplined by "hard and bitter . . . peace." Kennedy implicitly states how he leads by example.

Once the kinship is established, his message from "us" (all Americans) to them (all other nations) can logically follow: "Let the word go forth . . . to friend and foe. . . Let every nation know. . ." Other Americans, like him, share a patriotic duty to act in a unified way to achieve goals that are ours, not his alone.

When a speaker or writer uses pathos, they are appealing  to the emotions of their audience.  They are hoping that, through making the audience feel deeply about what they are speaking about, then the audience will side with them on the issue at hand.  For example, if you are trying to convince your teacher to boost your grade from an A- to an A, and emotional appeal might be, "My grandmother was really sick in the hospital this term, and so I was a bit distracted with that.  I tried my hardest to get my work done, but sometimes it was more important to be with her."  In this example, you are using pathos to pull on the heart strings of your teacher.

In Kennedy's speech, he uses pathos when he speaks of the many trials that their generation has gone through.  He mentions that they were

"born in this century, tempered by war, disciplined by hard and bitter peace."

Referring to war brings up all of the deaths that occurred, all of the suffering that they went through.  Referring to how hard it has been to have peace again, and to recover, it appeals to people's difficulties and emotions in regards to overcoming the tragedies of war.  So, he uses pathos, an appeal to the audience's emotions, hoping they will agree with him, commiserate, and be more willing to rally with what he is saying.

Ethos is defined differently, depending on the teacher.  Some teachers define it as how the speaker or writer uses his own reputation as a way to get you to believe what he is saying. I don't see any of that in this excerpt, so we'll go with the other definition, which refers to appealing to a community's sense of pride and uniqueness, in order to elicit a form of patriotism, which helps the audience to stand on your side.  In Kennedy's speech, he mentions that "we are heirs to that first revolution," appealling to Americans' united ancestry of the revolutionary war.  He continues by saying that we are "proud of our ancient heritage," which helps us to feel at one as Americans, wanting to unite together in the cause of "the success of liberty."  So, he appeals to our sense of community, to our uniqueness as Americans, and uses that to convince us that we need to fight for liberty.

I hope that those examples help; good luck!