Question

Is it possible for a distance-versus-time graph to be
a vertical line? Explain.

Answer 1

No.  If time is the horizontal axis and distance is the vertical axis, then
it is not possible for a distance-vs-time graph to be a vertical line.

A vertical line would mean:

-- the object was at all distances at the same time,

-- it moved from any location to any other location in no time, and

-- it moved with infinite speed.

Even light doesn't do that.  A distance-vs-time graph for light is
not a vertical line.  It's a slanted line with slope of  (3 x 10⁸) m/s.
Purty durn steep, but not vertical.

Answer 2

No, because time takes place on the x-axis and time never stops, so time would have to stop in order for it to be a vertical line.