Move on, move and move ahead - interchangeable?

English as a Second Language English Vocabulary, Grammar and Idioms
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1/Do move on , move and move ahead have the same meaning and are they interchangeable?If not, what is the difference in meaning btw them?

Ex:
Time is moving on. =Time is moving on.= Time is moving ahead. ?

Things are not moving as fast as I hoped.=Things are not moving on as fast as I hoped.=

Things are not moving ahead as fast as I hoped. ?

2/ It is sure that increase and grow can’t be used in these 3 sentences. Right?

Q

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Generally speaking, I would not consider move, move on and move ahead to be interchangeable.

These two sentences are unnatural:

  • Time is moving ahead.
  • Things are not moving [color=red]on as fast as I hoped.

No, increase and grow definitely do not work at all in those sentences.