Thanks for all the comments everyone, and thank you also Tom Wolsky for your great tutorial books and DVDs that have helped me to gain some competence with Final Cut. I recommend them highly to anyone learning the program.
To shed some light on the purpose of my original post, the project I'm working on contains both video footage and still images. In this video I'm demonstrating how to paint pictures, while using still images of historic paintings as examples of how the old-time painters did things, compared to what I'm doing now.
So in this video I alternate from live demonstrations of painting, to still images of old paintings, slowly panning and zooming around the old paintings and stopping to analyze portions of them.
I find that there is something comfortable and soothing about good pan/zooms as compared to the unsettling feelings and irritation caused by watching jerky starts and stops, with unnatural acceleration and deceleration between.
You have all made it clear to me (thanks again) that it is a matter of the mathematics involved in Final Cut's treatment of pan/zooms that makes it hard to get smooth movements of that type in FC. I still think it's odd that I can get wonderful pan/zooms from a cheapie little program like Photo-to-Movie but not a pro application like Final Cut, but at least PTM can get the job done for me, although it is a slowdown to have to use it. I first have to create the pan/zooms on still images in PTM and then export them as DV clips to drop into Final Cut. If a pan/zoom then needs adjustment, I have to throw the clip away, go back to PTM and modify the movement, and then export a fresh clip. Very slow.
By the way, I visited the Photo to Movie website, which I haven't done for a long time, and I see that the price of the program has now doubled to $50. The authors have apparently gotten big ideas and have added transitions, titles, and other kinds of editing besides just movement. On their demo webpage <http://tinyurl.com/yfej3j4> you can see sample pans and zooms created by the program. The third sample movie down from the top, with the zebras, shows some of the types of motion I'm after, such as the scene that zooms gently in on the turtle's head or the dog near the end of that movie. Note how smooth the starts/stops are.
In my own YouTube movie <http://tinyurl.com/yh8hl38>, which I created in Final Cut in 2008, the paintings that leap out at you with music at the beginning were also created in Photo to Movie and dropped into Final Cut. In that case the motion is almost violent, and no doubt I could have done it just as easily in Final Cut, but at that time I was new to keyframing in Final Cut and had gotten so accustomed to the ease of doing such things in PTM that I used it for that too. A few minutes further along in that video you can see the kind of gentle pan/zooming by PTM that I'm trying to create again now in a new video. My failed attempts to do it in Final Cut a couple days ago are what led me to ask for help here.
Maybe if I can gain a better grasp of Motion 2 I could do better with it than my first attempt yesterday, and I could also also round-trip between Motion and Final Cut to quickly adjust the movements, but I just don't know the program well enough yet to do that. I'll search for tutorials and demo movies on Motion. Someone above has also said that Motion 2 is inferior to version 3 in this respect, and I don't have 3, so I guess I'm stuck with Photo to Movie for the present to get smooth pan/zooms.
Thanks again everyone for all the enlightenment on this subject.
Tom B.