Question

on a graph of $v_x$ versus time, what quantity does the slope of the graph represent? multiple choice the total distance. the x-component of the displacement. the instantaneous speed. the x-component of the acceleration.

Explanation:

In a velocity - time ($v_x - t$) graph, the slope is calculated as $\frac{\Delta v_x}{\Delta t}$. By the definition of acceleration, $a_x=\frac{\Delta v_x}{\Delta t}$, so the slope represents the x - component of acceleration. Total distance is the area under a speed - time graph, displacement's x - component is the area under a $v_x - t$ graph, and instantaneous speed is the value of $v_x$ at a given time.

Answer:

The x - component of the acceleration.