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(a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PY PW POY

(a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PY PW POY

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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Question
In the previous Problem Set question, we started looking at the position function s (t), the position of an object at time t. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time t is s (t), then the position at time h later is s (t + h). The average velocity (speed) during that additional time (s(t+h)-s(t)) h his If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h→0, i.e. the derivative s' (t). Use this function in the model below for the velocity function v (t). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = v' (t) = s″ (t). S Problem Set question: A particle moves according to the position function s (t) = e4t sin (5t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) =
Transcribed Image Text:In the previous Problem Set question, we started looking at the position function s (t), the position of an object at time t. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time t is s (t), then the position at time h later is s (t + h). The average velocity (speed) during that additional time (s(t+h)-s(t)) h his If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h→0, i.e. the derivative s' (t). Use this function in the model below for the velocity function v (t). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a (t) = v' (t) = s″ (t). S Problem Set question: A particle moves according to the position function s (t) = e4t sin (5t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) =
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