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, 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) = e3t sin (5t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) (b) Find the acceleration function. a (t) =
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, 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) = e3t sin (5t). Enclose arguments of functions in parentheses. For example, sin (2t). (a) Find the velocity function. v (t) (b) Find the acceleration function. a (t) =
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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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 tis 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,
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) = e3t sin (5t).
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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