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Problem Set question: A particle moves according to the position function s (t) = et sin (6t). %3D Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function.

Problem Set question: A particle moves according to the position function s (t) = et sin (6t). %3D Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...
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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 veloocity 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 is 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). The acceleration is the rate of change of velocity, o 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) = e" sin Enclose arguments of functions in parentheses. For example, sin (2t) (a) Find the velocity function. a Va Ja| sin (a) 7 sin ( 6 t +6 cos 6 Submit Assignment Quit & Save Вack Question Menu -
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 veloocity 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 is 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). The acceleration is the rate of change of velocity, o 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) = e" sin Enclose arguments of functions in parentheses. For example, sin (2t) (a) Find the velocity function. a Va Ja| sin (a) 7 sin ( 6 t +6 cos 6 Submit Assignment Quit & Save Вack Question Menu -
7 sın 6 t + 6 cos ( 6 v (t) = (b) Find the acceleration function. la| sin (a) b 7 t e 13 sin 6 t) +48 cos 6 t a (t) =
Transcribed Image Text:7 sın 6 t + 6 cos ( 6 v (t) = (b) Find the acceleration function. la| sin (a) b 7 t e 13 sin 6 t) +48 cos 6 t a (t) =
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