There are some cases where distance time graph of a particle is vertical . so could you tell me when it is

-- If time is the horizontal axis and distance is the vertical axis, then it's not possible
for the particle's distance/time graph to be a vertical line.  That would indicate that
the particle covered some distance in zero time, indicating infinite speed.

-- If distance is the horizontal axis and time is the vertical axis, and the particle's
distance/time graph is a vertical line, then that indicates that the particle's distance
doesn't change with time. In other words, the particle is at rest, and its speed is zero.