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A particle moves according to the position function s(t) = e2t sin (7t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) (b) Find the acceleration function. a (t) 19

A particle moves according to the position function s(t) = e2t sin (7t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) (b) Find the acceleration function. a (t) 19

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 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) (s(t+h)-s(t)) h during that additional time 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, 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). Problem Set question: A particle moves according to the position function s(t) = e²t sin (7t). 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) (s(t+h)-s(t)) h during that additional time 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, 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). Problem Set question: A particle moves according to the position function s(t) = e²t sin (7t). 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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