The correct answer to the question is option 2, which states that the time versus distance graph of an object at rest is horizontal.

To understand this, we need to consider the definition of an object at rest. When an object is at rest, it means that it is not moving. Therefore, its position does not change over time. In other words, the distance traveled by the object remains constant.

A time versus distance graph represents the relationship between the time elapsed and the corresponding distance traveled. In the case of an object at rest, since the distance traveled is constant, the graph would be a straight line that is parallel to the x-axis, which represents time.

Option 1, stating that the graph is vertical, does not accurately represent an object at rest because a vertical line would indicate a constant change in time but a continuously changing distance.

Option 3, suggesting a 45° positive slope, and option 4, suggesting a 45° negative slope, both indicate movement, which contradicts the concept of an object at rest.

Therefore, the correct answer is option 2, indicating a horizontal graph.