Question

is it possible particle at x=0 still be moving?

Answer 1

of course! it can move! vertically. either upward or downward even if x=0. the value of its y is the one that is changing

Answer 2

True! And that's the highlight for movement while the particle stays at \(x=0\). Another point is that it can go from \(-x\) to \(+x\) (some negative \(x\) and some positive \(x\)), and be moving when it hits \(x=0\), right? Mathematically, you might say it takes two points to have movement... But if they're infinitely close to \(x=0\), it's similar!

Overall, definitely yes. Reference @fab_camie 's post for surely good reasons!