Question

the graph shows the motion of a mouse. mouses position vs. time. at what time does the mouse get back to where he started? at t = 10s, how far has the mouse moved? what is the slope of the line from t = 25s to t = 35s? what information does the slope this line tell you about the mouse?

Explanation:

Step1: Determine initial and final position for first - part

The initial position at \(t = 0\) is \(x_0=0\) m. From the graph, at \(t = 10\) s, the position \(x_1\) can be read. The position at \(t = 10\) s is \(x_1 = 20\) m. The distance moved \(\Delta x=x_1 - x_0\).
\(\Delta x=20 - 0=20\) m

Step2: Calculate slope for second - part

The slope \(m\) of a line in a position - time graph is given by \(m=\frac{\Delta x}{\Delta t}\). For \(t_1 = 25\) s and \(t_2 = 35\) s, the position at \(t_1\) is \(x_{t_1}=10\) m and at \(t_2\) is \(x_{t_2}=30\) m.
\(m=\frac{x_{t_2}-x_{t_1}}{t_2 - t_1}=\frac{30 - 10}{35 - 25}=\frac{20}{10}=2\) m/s. The slope represents the velocity of the mouse in this time - interval.

Step3: Find time for third - part

The mouse starts at \(x = 0\) m. To get back to the starting position, we need to find the time when \(x = 0\) again. Looking at the graph, the mouse reaches \(x = 0\) at \(t = 30\) s.

Answer:

1. At \(t = 10\) s, the mouse has moved 20 m.
2. The slope of the line from \(t = 25\) s to \(t = 35\) s is 2 m/s, which represents the velocity of the mouse in this time - interval.
3. The mouse gets back to where it started at \(t = 30\) s.