Fast is more difficult because it is hard to time it. But one of the easier way to CATCH something to shoot something repetitious (like a juggler, or somebody throwing a yo-yo, helicopter hovering but with the rotor blade absolutely frozen).
As for slow, you are looking for blur. So it would be DIFFERENT if something is blurred + not blurred. So you can have somebody stand ABSOLUTELY still while everybody else is moving around.
Then there is the camera blur:
http://www.photoshopessentials.com/images/photo-effects/ghosting/image-motion-blur.jpg
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Then you can mix slow shutter + flash to get blur and freezed action
http://farm4.static.flickr.com/3039/2863529422_224d733f02.jpg
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professors love it when you make them think. So you can get an image where it is difficult to tell if it was fast or slow shutter, they would like that. EX: SMOKE. You can shoot the slow moving smoke in slow shutter or fast.
http://www.sxc.hu/pic/m/a/as/asifthebes/735898_experimental_smoke_shot.jpg
Was that take with fast or slow shutter?
Good luck...