Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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I need help please
![In the previous Problem Set question, we started looking at the position function & (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 t is a (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time
(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,
l.e. the derivative s' (t). Use this function in the model below for the velocity function (t)
his
h
The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modéled with the derivative of the velocity
function, or the second derivative of the position function a (4) -(t)- " (t).
Problem Set question:
A particle moves according to the position functions (t) - et sin (8t).
17t
Enclose arguments of functions in parentheses. For example, sin (27)
(a) Find the velocity function.
a
b
√a
33
a
75
7t
27 [7 sin (8 7) + 8 cos (8)]
e
t
Q Search
sin (a)
112
Submit Assignment
Quit & Save](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5a78c13-da5a-4255-8b88-63fe3a182f48%2Feefbed01-33cc-494c-89c2-a220384fe764%2F9jwooco_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the previous Problem Set question, we started looking at the position function & (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 t is a (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time
(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,
l.e. the derivative s' (t). Use this function in the model below for the velocity function (t)
his
h
The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a (t) can be modéled with the derivative of the velocity
function, or the second derivative of the position function a (4) -(t)- " (t).
Problem Set question:
A particle moves according to the position functions (t) - et sin (8t).
17t
Enclose arguments of functions in parentheses. For example, sin (27)
(a) Find the velocity function.
a
b
√a
33
a
75
7t
27 [7 sin (8 7) + 8 cos (8)]
e
t
Q Search
sin (a)
112
Submit Assignment
Quit & Save
![(a) Find the velocity function.
v (t) =
a (t) =
a
b
(b) Find the acceleration function.
ab
va
e
7 [7 sin (8t) + 8 cos (8)]
a
b
a
√a
a
sin (a)
75
sin (a)
t
e
7 [112 cos (8t)-15şin (8t)]
E
?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5a78c13-da5a-4255-8b88-63fe3a182f48%2Feefbed01-33cc-494c-89c2-a220384fe764%2Febu2fi8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Find the velocity function.
v (t) =
a (t) =
a
b
(b) Find the acceleration function.
ab
va
e
7 [7 sin (8t) + 8 cos (8)]
a
b
a
√a
a
sin (a)
75
sin (a)
t
e
7 [112 cos (8t)-15şin (8t)]
E
?
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