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? where the mouse is located. it tells you nothing about the mouse, it is just a number. how far the mouse has moved. the velocity of the mouse

Explanation:

Step1: Recall slope - velocity relation

In a position - time graph, the slope of the line represents the velocity of the object.

Step2: Analyze slope from t = 25s to t = 35s

Let's assume two points on the line from t = 25s to t = 35s. If the position at t = 25s is \(x_1\) and at t = 35s is \(x_2\), the slope \(m=\frac{x_2 - x_1}{35 - 25}\). The slope gives the velocity of the mouse during this time - interval.

Step3: Find distance moved at t = 10s

We need to find the change in position from t = 0s to t = 10s. If the initial position \(x_0=0\) and the position at t = 10s is \(x_{10}\), the distance moved \(d=x_{10}-x_0\). We read the position value from the graph at t = 10s.

Step4: Determine time to return to starting point

The starting point is at position \(x = 0\). We look for the time on the x - axis when the position value on the y - axis returns to 0.

Answer:

1. The slope of the line in a position - time graph tells you the velocity of the mouse.
2. To find the slope from t = 25s to t = 35s, use the formula \(m=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t=35 - 25 = 10s\). Read the position values from the graph at t = 25s and t = 35s to calculate \(\Delta x\).
3. Read the position value at t = 10s from the graph. If the initial position at t = 0s is 0, the distance moved is equal to this position value.
4. Look for the time on the x - axis when the position value on the y - axis is 0 again to find the time when the mouse gets back to where it started.