the graph shows the motion of a mouse. mouses position vs. time. at what time does the mouse get back to…

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?

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?

Answer

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.