### Analyzing Motion through Graphs#### Instructions:A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the average velocity in the following time intervals.#### Graph Description:The graph plotted below shows the position (x) in meters (m) on the y-axis versus time (t) in seconds (s) on the x-axis. The graph starts at the origin (0,0) and proceeds through the following points:- From (0,0) to (2,8)- Then from (2,8) to (4,4)- From (4,4) to (5,4)- Then from (5,4) to (6,-2)- Finally from (6,-2) to (7, -5)#### Time Intervals and Average Velocity:Calculate the average velocity in the given time intervals by using the formula:\[ \text{Average Velocity} = \frac{\text{Change in Position} (\Delta x)}{\text{Change in Time} (\Delta t)} \]1. **(a) 0 to 2.00 s** - \( \Delta t = 2.00 \text{ s} \) - \( \Delta x = x(2.00\,s) - x(0\,s) = 8\, m - 0\, m \) - Average velocity = \( \frac{8\, m}{2.00\, s} \)2. **(b) 0 to 4.00 s** - \( \Delta t = 4.00 \text{ s} \) - \( \Delta x = x(4.00\,s) - x(0\,s) = 4\, m - 0\, m \) - Average velocity = \( \frac{4\, m}{4.00\, s} \)3. **(c) 2.00 s to 4.00 s** - \( \Delta t = 4.00 \text{ s} - 2.00 \text{ s} \) - \( \Delta x = x(4.00\,s) - x(2.00\,s) = 4\, m - 8\, m \) - Average velocity = \( \frac{4\, m - 8\, m

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A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the average velocity in the following time intervals. х (m) 10 2 Lt (s) 1 2 3 4 5 6 7 8 -2 (a) 0 to 2.00 s m/s (b) 0 to 4.00 s m/s (c) 2.00 s to 4.00 s m/s

A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the average velocity in the following time intervals. х (m) 10 2 Lt (s) 1 2 3 4 5 6 7 8 -2 (a) 0 to 2.00 s m/s (b) 0 to 4.00 s m/s (c) 2.00 s to 4.00 s m/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

### Analyzing Motion through Graphs

#### Instructions:
A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the average velocity in the following time intervals.

#### Graph Description:
The graph plotted below shows the position (x) in meters (m) on the y-axis versus time (t) in seconds (s) on the x-axis. The graph starts at the origin (0,0) and proceeds through the following points:
- From (0,0) to (2,8)
- Then from (2,8) to (4,4)
- From (4,4) to (5,4)
- Then from (5,4) to (6,-2)
- Finally from (6,-2) to (7, -5)

#### Time Intervals and Average Velocity:
Calculate the average velocity in the given time intervals by using the formula:
\[ \text{Average Velocity} = \frac{\text{Change in Position} (\Delta x)}{\text{Change in Time} (\Delta t)} \]

1. **(a) 0 to 2.00 s**
- \( \Delta t = 2.00 \text{ s} \)
- \( \Delta x = x(2.00\,s) - x(0\,s) = 8\, m - 0\, m \)
- Average velocity = \( \frac{8\, m}{2.00\, s} \)

2. **(b) 0 to 4.00 s**
- \( \Delta t = 4.00 \text{ s} \)
- \( \Delta x = x(4.00\,s) - x(0\,s) = 4\, m - 0\, m \)
- Average velocity = \( \frac{4\, m}{4.00\, s} \)

3. **(c) 2.00 s to 4.00 s**
- \( \Delta t = 4.00 \text{ s} - 2.00 \text{ s} \)
- \( \Delta x = x(4.00\,s) - x(2.00\,s) = 4\, m - 8\, m \)
- Average velocity = \( \frac{4\, m - 8\, m

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