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

-- 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.

when the body is in rest or in constant speed