Is distance traveled by a moving train qualitative discrete continuous or na?

Continuous. Discrete values are values like 1, 2, 3, 4, etc. - they're values that are distinct, and typically there's some idea of a next and a previous value. When we're counting whole numbers, there's a definitive answer to which number comes after, and which number comes before. With continuous values, there's no real "next" or "last" value.

Motion is measured with continuous values; a train might move 300 yards in 1 minute, but we can look at smaller and smaller chunks of time to keep getting shorter and shorter distances. There is no "next" distance the train moves after those 300 yards - it just doesn't make sense for there to be.

It's also measured quantitatively, not qualitatively. This just means that we can use numerical values to measure it, rather than other descriptors like color, smell, or taste.