### Educational DescriptionThe given text is a problem statement for analyzing a velocity vs. time graph to determine the position, velocity, and acceleration of a particle at a specific time.#### Problem Statement:The graph on the right shows velocity vs. time. The particle at time \( t = 0 \) is positioned at \( X_0 = 15 \). What is the position, velocity, and acceleration at \( t = 8.0 \) seconds?#### Graph Explanation:- **Axes**: - The vertical axis represents velocity \( v_x \) in meters per second (m/s), ranging from -10 to 10. - The horizontal axis represents time \( t \) in seconds (s), ranging from 0 to 12.- **Graph Characteristics**: - The graph starts at \( t = 0 \) with a velocity of 10 m/s. - Velocity decreases linearly to 0 m/s at \( t = 6 \) seconds. - From \( t = 6 \) to \( t = 8 \) seconds, velocity continues to decrease linearly to -5 m/s. - From \( t = 8 \) seconds onward, the velocity remains constant at -5 m/s.#### Mathematical Analysis:- **Velocity at \( t = 8.0 \) seconds**: -5 m/s (as observed from the graph).- **Acceleration**: The slope of the velocity-time graph indicates acceleration. From \( t = 0 \) to \( t = 6 \), a negative slope indicates constant deceleration.- **Position Calculation**: Use the initial position \( X_0 = 15 \) and integrate the area under the velocity-time graph to find the position at \( t = 8.0 \) seconds.

Answered: Image /qna-images/answer/a950df87-b596-43fe-8ec2-7f1ea4543e82.jpg

Answered: The graph at right shows velocity vs.…

The graph at right shows velocity vs. time. The particle at t=0 was positioned at Xo = 15. What is the position, velocity and acceleration at t=8.0 s? V. (m/s) 10- 5 0 -5 2 4 -t(s) 6 8 10 12

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

### Educational Description

The given text is a problem statement for analyzing a velocity vs. time graph to determine the position, velocity, and acceleration of a particle at a specific time.

#### Problem Statement:
The graph on the right shows velocity vs. time. The particle at time \( t = 0 \) is positioned at \( X_0 = 15 \). What is the position, velocity, and acceleration at \( t = 8.0 \) seconds?

#### Graph Explanation:
- **Axes**:
- The vertical axis represents velocity \( v_x \) in meters per second (m/s), ranging from -10 to 10.
- The horizontal axis represents time \( t \) in seconds (s), ranging from 0 to 12.

- **Graph Characteristics**:
- The graph starts at \( t = 0 \) with a velocity of 10 m/s.
- Velocity decreases linearly to 0 m/s at \( t = 6 \) seconds.
- From \( t = 6 \) to \( t = 8 \) seconds, velocity continues to decrease linearly to -5 m/s.
- From \( t = 8 \) seconds onward, the velocity remains constant at -5 m/s.

#### Mathematical Analysis:
- **Velocity at \( t = 8.0 \) seconds**: -5 m/s (as observed from the graph).
- **Acceleration**: The slope of the velocity-time graph indicates acceleration. From \( t = 0 \) to \( t = 6 \), a negative slope indicates constant deceleration.
- **Position Calculation**: Use the initial position \( X_0 = 15 \) and integrate the area under the velocity-time graph to find the position at \( t = 8.0 \) seconds.

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