Question

1. what would the position - time graph for a stationary object look like? a horizontal (zero slope) line a vertical (undefined slope) line a line with negative slope a line with positive slope

Explanation:

In a position - time graph, the slope represents velocity ($v=\frac{\Delta x}{\Delta t}$). For a stationary object, the position ($x$) does not change over time ($t$), so $\Delta x = 0$. Then the slope $v=\frac{0}{\Delta t}=0$. A horizontal line has a slope of 0. A vertical line would imply an infinite change in position over zero time (which is impossible in reality for a position - time graph as it violates the concept of a function, since for a given time there should be a unique position). A line with negative slope means the object is moving in the negative direction (position is decreasing with time), and a line with positive slope means the object is moving in the positive direction (position is increasing with time).

Answer:

a horizontal (zero slope) line