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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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