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15. s(t) = 9-9 сos (лt/3), 0≤t≤5 t 16 s(t) t> 0

15. s(t) = 9-9 сos (лt/3), 0≤t≤5 t 16 s(t) t> 0

Calculus: Early Transcendentals
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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#15 a-d only 

do not do "e"

### Calculus: Position, Velocity, and Acceleration This section focuses on understanding how the position function \( s(t) \) of a particle moving along a coordinate line is related to its velocity and acceleration. The exercises aim to apply calculus concepts to analyze the motion of the particle over time. #### Exercises 13-18 **Problem Statement:** The function \( s(t) \) describes the position of a particle moving along a coordinate line, where \( s \) is in feet and \( t \) is in seconds. 1. **Find the velocity and acceleration functions.** 2. **Find the position, velocity, speed, and acceleration at time \( t = 1 \).** 3. **Determine when the particle is stopped.** 4. **Analyze when the particle is speeding up or slowing down.** 5. **Calculate the total distance traveled by the particle from time \( t = 0 \) to time \( t = 5 \).** **Equations:** - \( s(t) = t^3 - 3t^2, \quad t \geq 0 \) - \( s(t) = t^4 - 4t^2 + 4, \quad t \geq 0 \) - \( s(t) = 9 - 9 \cos(\pi t/3), \quad 0 \leq t \leq 5 \) - \( s(t) = \frac{t}{2}, \quad t \geq 0 \) - \( s(t) = (t^2 + 8)e^{-t/3}, \quad t \geq 0 \) - \( s(t) = \frac{1}{4} t^2 - \ln(t + 1), \quad t \geq 0 \) #### Exercise 19 Consider the function \( s(t) = t/(t^2 + 5) \) representing the position of a particle over time. - **(a)** Use graphs to estimate when the particle first reverses its direction, then find this time exactly. - **(b)** Determine the exact position of the particle when it reverses its direction. - **(c)** Use graphs to estimate and find the time intervals during which the particle is speeding up and slowing down. ### Graphs and Analysis: - **Graphing Tools:** Use a graphing utility to visualize the
Transcribed Image Text:### Calculus: Position, Velocity, and Acceleration This section focuses on understanding how the position function \( s(t) \) of a particle moving along a coordinate line is related to its velocity and acceleration. The exercises aim to apply calculus concepts to analyze the motion of the particle over time. #### Exercises 13-18 **Problem Statement:** The function \( s(t) \) describes the position of a particle moving along a coordinate line, where \( s \) is in feet and \( t \) is in seconds. 1. **Find the velocity and acceleration functions.** 2. **Find the position, velocity, speed, and acceleration at time \( t = 1 \).** 3. **Determine when the particle is stopped.** 4. **Analyze when the particle is speeding up or slowing down.** 5. **Calculate the total distance traveled by the particle from time \( t = 0 \) to time \( t = 5 \).** **Equations:** - \( s(t) = t^3 - 3t^2, \quad t \geq 0 \) - \( s(t) = t^4 - 4t^2 + 4, \quad t \geq 0 \) - \( s(t) = 9 - 9 \cos(\pi t/3), \quad 0 \leq t \leq 5 \) - \( s(t) = \frac{t}{2}, \quad t \geq 0 \) - \( s(t) = (t^2 + 8)e^{-t/3}, \quad t \geq 0 \) - \( s(t) = \frac{1}{4} t^2 - \ln(t + 1), \quad t \geq 0 \) #### Exercise 19 Consider the function \( s(t) = t/(t^2 + 5) \) representing the position of a particle over time. - **(a)** Use graphs to estimate when the particle first reverses its direction, then find this time exactly. - **(b)** Determine the exact position of the particle when it reverses its direction. - **(c)** Use graphs to estimate and find the time intervals during which the particle is speeding up and slowing down. ### Graphs and Analysis: - **Graphing Tools:** Use a graphing utility to visualize the
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