Question

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?

Answer 1

Answer:

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:

$m=\frac{\Delta y}{\Delta x}$

where

$\Delta y$ is the increment in the y-variable

$\Delta t$ is the increment in the x-variable

However, we have that:

$\Delta y$ corresponds to $\Delta r$, the change in position of the object

$\Delta x$ corresponds to the change in time, $\Delta t$

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

$m=\frac{\Delta r}{\Delta t}=v$

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.

Answer 2

Answer: slope of the line is zero

Explanation: