Question

interpreting a motion graph
multiple - choice question
what is the slope from the 50 minute mark to the 70 minute mark?
14.4 mph
10 mph
0 mph

Explanation:

Step1: Identify the formula for slope

The slope $m$ of a line is given by $m=\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in displacement and $\Delta x$ is the change in time. In the context of a displacement - time graph, the slope represents velocity.

Step2: Determine the change in displacement and time

From the 50 - minute mark to the 70 - minute mark, the time interval $\Delta x=70 - 50=20$ minutes. Since the displacement does not change (the graph is a horizontal line segment in this interval), $\Delta y = 0$ miles.

Step3: Calculate the slope

Using the slope formula $m=\frac{\Delta y}{\Delta x}$, substituting $\Delta y = 0$ and $\Delta x=20$ minutes. First, convert 20 minutes to hours: 20 minutes $=\frac{20}{60}=\frac{1}{3}$ hours. Then $m=\frac{0}{\frac{1}{3}} = 0$ mph.

Answer:

0 mph