The displacement of a particle on a vibrating string is given by the function below, where t is measured in seconds (s) and s in centimeters (cm). 1. Find the velocity function. Answer: v(t) = 2. Find the acceleration function. Answer: a(t) = 3. Find the position at time t = . Include the units in your answer. 10 Answer: I () (help with Units) 4. Find the velocity at time t = . Include the units in your answer. Answer: v() = = 5. Find the acceleration at time t = 10 Include the units in your answer. Answer: a ¹ (1) 6. In what direction is the object moving at time t = 10 Answer: left or right? s(t) = 9+ sin(10πt) 4°
The displacement of a particle on a vibrating string is given by the function below, where t is measured in seconds (s) and s in centimeters (cm). 1. Find the velocity function. Answer: v(t) = 2. Find the acceleration function. Answer: a(t) = 3. Find the position at time t = . Include the units in your answer. 10 Answer: I () (help with Units) 4. Find the velocity at time t = . Include the units in your answer. Answer: v() = = 5. Find the acceleration at time t = 10 Include the units in your answer. Answer: a ¹ (1) 6. In what direction is the object moving at time t = 10 Answer: left or right? s(t) = 9+ sin(10πt) 4°
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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![**Educational Exercise: Calculating Velocity and Acceleration**
The displacement of a particle on a vibrating string is given by the function below, where \( t \) is measured in seconds (s) and \( s \) in centimeters (cm).
\[ s(t) = 9 + \frac{1}{4} \sin(10\pi t) \]
### Problems:
1. **Find the velocity function.**
- Answer: \( v(t) = \) [Input box]
2. **Find the acceleration function.**
- Answer: \( a(t) = \) [Input box]
3. **Find the position at time \( t = \frac{1}{10} \). Include the units in your answer.**
- Answer: \( x\left(\frac{1}{10}\right) = \) [Input box] (help with [Units](#))
4. **Find the velocity at time \( t = \frac{1}{10} \). Include the units in your answer.**
- Answer: \( v\left(\frac{1}{10}\right) = \) [Input box]
5. **Find the acceleration at time \( t = \frac{1}{10} \). Include the units in your answer.**
- Answer: \( a\left(\frac{1}{10}\right) = \) [Input box]
6. **In what direction is the object moving at time \( t = \frac{1}{10} \).**
- Answer: [Dropdown box: left or right?]
This exercise involves understanding the derivative of a sinusoidal function to determine velocity and acceleration, crucial in the study of harmonic motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d728491-ca3a-470b-9076-be2816d1a071%2F89f51c35-81ce-4e0a-b98a-dca5df1a23f4%2F8bz9nq_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Exercise: Calculating Velocity and Acceleration**
The displacement of a particle on a vibrating string is given by the function below, where \( t \) is measured in seconds (s) and \( s \) in centimeters (cm).
\[ s(t) = 9 + \frac{1}{4} \sin(10\pi t) \]
### Problems:
1. **Find the velocity function.**
- Answer: \( v(t) = \) [Input box]
2. **Find the acceleration function.**
- Answer: \( a(t) = \) [Input box]
3. **Find the position at time \( t = \frac{1}{10} \). Include the units in your answer.**
- Answer: \( x\left(\frac{1}{10}\right) = \) [Input box] (help with [Units](#))
4. **Find the velocity at time \( t = \frac{1}{10} \). Include the units in your answer.**
- Answer: \( v\left(\frac{1}{10}\right) = \) [Input box]
5. **Find the acceleration at time \( t = \frac{1}{10} \). Include the units in your answer.**
- Answer: \( a\left(\frac{1}{10}\right) = \) [Input box]
6. **In what direction is the object moving at time \( t = \frac{1}{10} \).**
- Answer: [Dropdown box: left or right?]
This exercise involves understanding the derivative of a sinusoidal function to determine velocity and acceleration, crucial in the study of harmonic motion.
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