A.The table indicates that a(1)= 2m/s. What does that tell you about the velocity B. The table indicates that. a(3) =-1 m/s. What does this tell you about velocity. C. When is the velocity of the train going to be the greatest. Explain your reasoning.
A.The table indicates that a(1)= 2m/s. What does that tell you about the velocity B. The table indicates that. a(3) =-1 m/s. What does this tell you about velocity. C. When is the velocity of the train going to be the greatest. Explain your reasoning.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A.The table indicates that a(1)= 2m/s. What does that tell you about the velocity
B. The table indicates that. a(3) =-1 m/s. What does this tell you about velocity.
C. When is the velocity of the train going to be the greatest. Explain your reasoning.
Transcribed Image Text:Here is a transcription of the handwritten text from the image with a detailed explanation suitable for an educational website:
---
### Assumptions and Data Table for Motion Analysis
**Assumptions:**
- Assume \( t = 0 \) was at \( 0 \, \text{m/s} \)
**Data Table:**
| \( t \) (seconds) | \( a(t) \) (meters/second\(^2\)) |
|:-----------------:|:-------------------------------:|
| 0 | 3 |
| 1 | 2 |
| 2 | 1 |
| 3 | -1 |
| 4 | -2 |
This table provides the acceleration values (in meters per second squared) at various time intervals (in seconds). The initial condition given is that at time \( t = 0 \), the velocity was \( 0 \, \text{m/s} \).
### Explanation:
- At \( t = 0 \) seconds, the acceleration \( a(t) \) is 3 \( \text{m/s}^2 \).
- At \( t = 1 \) second, the acceleration decreases to 2 \( \text{m/s}^2 \).
- At \( t = 2 \) seconds, the acceleration is 1 \( \text{m/s}^2 \).
- At \( t = 3 \) seconds, the acceleration becomes negative, \( -1 \, \text{m/s}^2 \).
- At \( t = 4 \) seconds, the acceleration further decreases to \( -2 \, \text{m/s}^2 \).
---
**Note:**
- Negative acceleration indicates deceleration.
This information is typically used in kinematics to determine the velocity and displacement of an object over time. The varying acceleration values can help in plotting acceleration vs. time graphs, which can then be integrated to find velocity vs. time and displacement vs. time graphs.
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