A particle moves according to the position function s (t) = e2t sin (3t). %3D

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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a) Find the velocity function

v(t)=

b) Find the acceleration function

a(t)=

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, 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 (3t).
Transcribed Image Text: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, 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 (3t).
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