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How to slow the shutter speed on point & shoot camera? - best ways to use a point and shoot camera

I was a user of modern digital SLR cameras (Nikon D40), but had to sell it for financial reasons. I buy a compact camera, not sure what type. but I wonder whether there are cameras or another in most cameras to be in a position to the shutter speed too slow? I am a big fan of getting shots or rivers, waterfalls, with slow shutter speeds, the effect of silk. is there a way you can do that for some cameras on the market?