**Displacement of the Dog**

The displacement of an object is a vector quantity that refers to the change in position of the object from its initial position to its final position. It is different from the distance traveled, as displacement takes into account the direction of motion.

To calculate the displacement of the dog, we need to consider the distance it covers in each direction and the direction of motion.

**Given Information:**
- The dog runs along a straight railway track for 1 minute and covers a distance of 50 m.
- The dog then runs back along the track for 4 minutes and covers a distance of 250 m.
- The dog initially runs towards the west.

To solve this problem, we can break it down into two parts - the dog's motion towards the west and the dog's motion towards the east.

**Motion Towards the West:**
- The dog runs along the track for 1 minute and covers a distance of 50 m.
- Since the dog is running towards the west, we can assign this motion a negative value.
- Therefore, the displacement of the dog towards the west is -50 m.

**Motion Towards the East:**
- The dog runs back along the track for 4 minutes and covers a distance of 250 m.
- Since the dog is now running towards the east, we can assign this motion a positive value.
- Therefore, the displacement of the dog towards the east is +250 m.

**Total Displacement:**
To find the total displacement of the dog, we need to sum up the displacements in each direction. Since displacement is a vector quantity, we need to consider both magnitude and direction.

- Displacement towards the west: -50 m (magnitude) in the west (direction)
- Displacement towards the east: +250 m (magnitude) in the east (direction)

To calculate the total displacement, we subtract the displacement towards the west from the displacement towards the east:

Total Displacement = Displacement towards the east - Displacement towards the west
= +250 m - (-50 m)
= +250 m + 50 m
= +300 m

Therefore, the displacement of the dog is +300 m towards the east.

In conclusion, the dog covers a total displacement of +300 m towards the east when it initially runs towards the west.