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.