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6. A particle moves with position function S(t) = – 2? + 31, t0 [T:3] a) Determine the velocity of the motion at 3 seconds b) Determine the acceleration of the motion at 3 seconds

6. A particle moves with position function S(t) = – 2? + 31, t0 [T:3] a) Determine the velocity of the motion at 3 seconds b) Determine the acceleration of the motion at 3 seconds

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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**Problem 6.** A particle moves with position function \( S(t) = \frac{1}{4}t^4 - 2t^2 + 3t \), \( t \geq 0 \). a) Determine the velocity of the motion at 3 seconds. b) Determine the acceleration of the motion at 3 seconds. **Solution Explanation:** To solve this problem, we need to find the velocity and acceleration functions of a particle described by the given position function \( S(t) = \frac{1}{4}t^4 - 2t^2 + 3t \). 1. **Velocity**: The velocity of a particle is the first derivative of the position function with respect to time \( t \). Calculate the derivative \( S'(t) \). 2. **Acceleration**: The acceleration of a particle is the derivative of the velocity function, or the second derivative of the position function. Calculate the derivative \( S''(t) \). Substitute \( t = 3 \) seconds into these derivative expressions to find the velocity and acceleration at this specific time.
Transcribed Image Text:**Problem 6.** A particle moves with position function \( S(t) = \frac{1}{4}t^4 - 2t^2 + 3t \), \( t \geq 0 \). a) Determine the velocity of the motion at 3 seconds. b) Determine the acceleration of the motion at 3 seconds. **Solution Explanation:** To solve this problem, we need to find the velocity and acceleration functions of a particle described by the given position function \( S(t) = \frac{1}{4}t^4 - 2t^2 + 3t \). 1. **Velocity**: The velocity of a particle is the first derivative of the position function with respect to time \( t \). Calculate the derivative \( S'(t) \). 2. **Acceleration**: The acceleration of a particle is the derivative of the velocity function, or the second derivative of the position function. Calculate the derivative \( S''(t) \). Substitute \( t = 3 \) seconds into these derivative expressions to find the velocity and acceleration at this specific time.
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