When you see a flat line on a position vs. time graph, what is the slope of this line? what does this tell you about motion of the object?

The slope of the line is zero

The object is at rest

Explanation:

The graph position vs time of an object represents the position of the object measured at different times.

The slope of this graph is given by:

where

is the increment in the y-variable

is the increment in the x-variable

However, we have that:

corresponds to , the change in position of the object

corresponds to the change in time,

Therefore, for a position-time graph the slope of the graph corresponds to the velocity of the object:

An object having a flat line on a position-time graph has a line with slope zero: therefore, its velocity is zero, and this means the object is at rest.