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

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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,
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).
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, 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) = eTt sin (2t).
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:Problem Set question: A particle moves according to the position function s (t) = eTt sin (2t). 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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Follow-up Question

In the previous Problem Set question, we started looking at the position function s(t)st, the position of an object at time  tt . Two important physics concepts are the velocity and the acceleration.

 

If the current position of the object at time tt is s(t)st, then the position at time hh later is s(t+h)st+h. The average velocity (speed) during that additional time hh is (s(t+h)−s(t))hst+h−sth . If we want to analyze the instantaneous velocity at time tt, this can be made into a mathematical model by taking the limit as h→0h→0, i.e. the derivative s′(t)s′t. Use this function in the model below for the velocity function v(t)vt.

 

The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t)at can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=v′(t)=s′′(t)at=v′t=s″t.

 

Problem Set question:

 

A particle moves according to the position function s(t)=e^5t sin(7t)

 

Enclose arguments of functions in parentheses. For example, sin(2t)

 

(a) Find the velocity function.

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