Question

1. motion sensors recorded the following data about a runner during a cross - country race. during which segment of the graph above did the runner have the greatest speed? clear all y w z x

Explanation:

Step1: Recall speed - position - time relationship

Speed $v=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position and $\Delta t$ is the change in time. On a position - time graph, the slope of the line segment represents the speed.

Step2: Analyze the slopes of segments

For segment W: Calculate the slope by choosing two points on the line. Let's say the change in position $\Delta x_W$ and change in time $\Delta t_W$. The slope $m_W=\frac{\Delta x_W}{\Delta t_W}$.
For segment X: Similarly, find two points, get $\Delta x_X$ and $\Delta t_X$, and the slope $m_X = \frac{\Delta x_X}{\Delta t_X}$.
For segment Y: Determine $\Delta x_Y$ and $\Delta t_Y$, and the slope $m_Y=\frac{\Delta x_Y}{\Delta t_Y}$.
For segment Z: Find $\Delta x_Z$ and $\Delta t_Z$, and the slope $m_Z=\frac{\Delta x_Z}{\Delta t_Z}$.
By visual inspection of the graph, we can see that the slope of segment W is the steepest among all the segments. A steeper slope on a position - time graph means a greater speed.

Answer:

B. W