A particle moves according to the position function s (t) = est sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PGT Pw
A particle moves according to the position function s (t) = est sin (4t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PGT Pw
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))
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,
h
i.e. the derivative s' (t). Use this function in the model below for the velocity function v (t).
his
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).
Problem Set question:
A particle moves according to the position function s (t) = eſt sin (4t).
Enclose arguments of functions in parentheses. For example, sin (2t).
(a) Find the velocity function.
v (t) =
(b) Find the acceleration function.
a (t) =
BS](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F890c6b0c-7e00-4a6b-b4b4-edad67d73083%2F98236051-1589-44e1-9c2e-a374d5c3ae03%2F7wzh8ob_processed.png&w=3840&q=75)
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))
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,
h
i.e. the derivative s' (t). Use this function in the model below for the velocity function v (t).
his
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).
Problem Set question:
A particle moves according to the position function s (t) = eſt sin (4t).
Enclose arguments of functions in parentheses. For example, sin (2t).
(a) Find the velocity function.
v (t) =
(b) Find the acceleration function.
a (t) =
BS
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