With a faster travelling object you can get the appropriate amount of motion blur with a faster shutterspeed and that seems to be earier in my experience.
This is a car doing about 140km/hr slowing for a fairly tight corner
Shutter speed is 1/60, f8
Same car but taken in different light conditions so this shot is at 1/40s. f4 (i didnt get many keepers at 1/40) The background looks better for conveying motion.
Cars are boring anyway because you get blurry wheels and thats about it (a glowing brake disc in the last one though)
Cyclists are more interesting because of their legs moving.
How about a Kayaker(ist?)
This one is taken a 1/10s so I'm suprised i got anything at all. I tried a couple of other paddlers at 1/30 but it didn't look good enoughimppression of motion.
This guy was really pushing hard so I probably could have done 1/15 for a bit less blur in the arms.
How about a kid on a swing? This might be a challenge because the speed of the pendulum is always changing and the path is curved.
I think the way to approach it might be to pick a point in the arc to take the shot which would be interesting (maybe halfway down on the backward swing, as the person's body will be parallel to the focus line) at then and just follow through that section of the arc clicking at that point of the swing.
I remember there was a compettion challenge over on DPreview a while ago and the winning entry was a vertical pan of a Cheetah leaping up a tree trunk. That was good but perhaps a little difficult to do in your neighbourhood..
edit : here it is
http://www.dpreview.com/challenges/Entry.aspx?ID=164624&View=Results&Rows=4