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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
I need help with (a) through (e)
![A particle moves according to a law of motion s = f(t), t> 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)
%3D
f(t) = t3 - 8t2 + 25t
%3D
(a) Find the velocity at time t.
v(t) =
ft/s
%3D
(b) What is the velocity after 1 second?
v(1) =
ft/s
%3D
(c) When is the particle at rest?
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
(e) Find the total distance traveled during the first 6 seconds.
ft
(f) Draw a diagram like this figure to illustrate the motion of the particle.
t = 0
S = 0
8.
t= -
8.
t =
3
1672
t = 0
|
S= 0
1672
S =
S =
27
27
S Type here to search
%S4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa699feee-67df-45a7-b712-d93645cac786%2Ffd4e3e49-2148-4072-8a8d-e18ee3660226%2Fj0kvuvv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A particle moves according to a law of motion s = f(t), t> 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)
%3D
f(t) = t3 - 8t2 + 25t
%3D
(a) Find the velocity at time t.
v(t) =
ft/s
%3D
(b) What is the velocity after 1 second?
v(1) =
ft/s
%3D
(c) When is the particle at rest?
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
(e) Find the total distance traveled during the first 6 seconds.
ft
(f) Draw a diagram like this figure to illustrate the motion of the particle.
t = 0
S = 0
8.
t= -
8.
t =
3
1672
t = 0
|
S= 0
1672
S =
S =
27
27
S Type here to search
%S4
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