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time based motion vs frame rate based motion

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Hello , I'm new to Game programmming, and I have been following Lazyfoo's SDL tutorials. My question is related to time based motion and frame rate based motion, basically which is better or appropriate depending on situations?. Could you give me an example where each of these methods are used?.

Another question I have is that, in lazyfoo's two Motion tutorials (FPS based and time based) The time based method showed a much smoother animation while the Frame rate based one was a little hiccupy, meaning you could clearly see the gap between the previous location of the dot and its current position when you compare the two programs.

As beginner which method should I stick to?(all I want is smooth animations).

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