(a) Find the velocity at time t. v(t) = ft/s (b) What is the velocity after 1 second? v(1) = ft/s (c) When is the particle at rest?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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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
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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ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning