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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![### Understanding Velocity at a Given Time
**Problem:**
Determine the velocity at \( t = 13 \) seconds.
**Solution:**
To find the velocity at a specific time from a position vs. time graph, you need to determine the slope of the line at that point.
**Graph Description:**
- **Axes:** The graph has the time (t) in seconds on the x-axis, ranging from 0 to 20 seconds, and position (pos) in meters on the y-axis, ranging from 0 to 50 meters.
- **Line Plot:** A straight line starts at the origin (0, 0) and passes through the point labeled \( (13\, \text{s}, 36\, \text{m}) \).
**Calculating Velocity:**
The velocity is the slope of the line, which can be calculated using the formula for slope:
\[
\text{Velocity} = \frac{\Delta \text{position}}{\Delta \text{time}}
\]
From the graph:
- Initial position at \( t = 0 \) is 0 meters.
- Final position at \( t = 13 \) seconds is 36 meters.
Thus, the change in position \(\Delta \text{position} = 36 - 0 = 36\) meters.
The change in time \(\Delta t = 13 - 0 = 13\) seconds.
\[
\text{Velocity} = \frac{36 \, \text{m}}{13 \, \text{s}} \approx 2.77 \, \text{m/s}
\]
Therefore, the velocity at \( t = 13 \) seconds is approximately \( 2.77 \, \text{m/s} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69d03f24-bad4-4ead-b3ae-1593ebe2e495%2F6a0bfdf6-02bd-4bf6-a56a-5376856559f2%2Ffkfjfws_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Velocity at a Given Time
**Problem:**
Determine the velocity at \( t = 13 \) seconds.
**Solution:**
To find the velocity at a specific time from a position vs. time graph, you need to determine the slope of the line at that point.
**Graph Description:**
- **Axes:** The graph has the time (t) in seconds on the x-axis, ranging from 0 to 20 seconds, and position (pos) in meters on the y-axis, ranging from 0 to 50 meters.
- **Line Plot:** A straight line starts at the origin (0, 0) and passes through the point labeled \( (13\, \text{s}, 36\, \text{m}) \).
**Calculating Velocity:**
The velocity is the slope of the line, which can be calculated using the formula for slope:
\[
\text{Velocity} = \frac{\Delta \text{position}}{\Delta \text{time}}
\]
From the graph:
- Initial position at \( t = 0 \) is 0 meters.
- Final position at \( t = 13 \) seconds is 36 meters.
Thus, the change in position \(\Delta \text{position} = 36 - 0 = 36\) meters.
The change in time \(\Delta t = 13 - 0 = 13\) seconds.
\[
\text{Velocity} = \frac{36 \, \text{m}}{13 \, \text{s}} \approx 2.77 \, \text{m/s}
\]
Therefore, the velocity at \( t = 13 \) seconds is approximately \( 2.77 \, \text{m/s} \).
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