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In the previous Problem Set question, we started looking at the position function (), the position of an object at fimet. 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 later is s(t+h). The average velocity (speed) during that additional time his ("(t+h)-a(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. L.e. the derivative a' (t). Use this function in the model below for the velocity function (t). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (1) can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=√(t)=s" (t). Problem set question: =e7t sin (21). A particle moves according to the position function (t) = Enclose arguments of functions in parentheses. For example, sin (21).

In the previous Problem Set question, we started looking at the position function (), the position of an object at fimet. 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 later is s(t+h). The average velocity (speed) during that additional time his ("(t+h)-a(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. L.e. the derivative a' (t). Use this function in the model below for the velocity function (t). The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (1) can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=√(t)=s" (t). Problem set question: =e7t sin (21). A particle moves according to the position function (t) = Enclose arguments of functions in parentheses. For example, sin (21).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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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In the previous Problem Set question, we started looking at the position functions (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 is as (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time his (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. i.e. the derivative a' (t). Use this function in the model below for the velocity function (). h 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) = ✔ (t) =" (t). Problem set question: A particle moves according to the position functions (t) = etsin (2). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = 2 (b) Find the acceleration function. a(t) |- |a| A |a| 24 T sin (a) sin (a) 8 8 ~ ~
Transcribed Image Text:In the previous Problem Set question, we started looking at the position functions (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 is as (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time his (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. i.e. the derivative a' (t). Use this function in the model below for the velocity function (). h 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) = ✔ (t) =" (t). Problem set question: A particle moves according to the position functions (t) = etsin (2). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) = 2 (b) Find the acceleration function. a(t) |- |a| A |a| 24 T sin (a) sin (a) 8 8 ~ ~
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