Yes―sort of. If displacement increases or decreases suddenly in an infinitely small point in time or a time interval that is too small to graph, a vertical line is used.
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infinite speed
No: not until instantaneous teleportation is discovered.
Object will change distance time graph when speed is changing. Distance time graph don't changed indicate of the stationary.
it will never be a vertical line as the slope is velocity and that would be infinite speed
Oh, dude, a horizontal line on a displacement-time graph represents an object standing still, not moving an inch. It's like when you're binge-watching Netflix and you haven't moved from the couch in hours - that's your horizontal line right there. So, yeah, it basically means zero movement, just chillin'.