A particle moves according to a law of motion s = f(t),t20, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t - 9t2 + 24t (a) Find the velocity (in ft/s) at time t. (3+-32+ 18+-24) t/s v(t) = (b) What is the velocity (in ft/s) afeer 1 second? v(1) = ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.)
A particle moves according to a law of motion s = f(t),t20, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t - 9t2 + 24t (a) Find the velocity (in ft/s) at time t. (3+-32+ 18+-24) t/s v(t) = (b) What is the velocity (in ft/s) afeer 1 second? v(1) = ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.)
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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30
30
30
20
20
20
10
10
10
4
5
-10
-10
10
30
20
a
10
- 10
(h) When is the particle speeding up? (Enter your answer using interval notation.)
When is it slowing down? (Enter your answer using interval notation.)
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Transcribed Image Text:A particle moves according to a law of motion s = f(t),t2 0, where t is measured in seconds ands in feet. (If an answer does not exist, enter DNE.)
f(t) = t3 - 9t2 + 24t
(a) Find the velocity (in ft/s) at time t.
v(t) =
+ 18 +-24) ft/s
(b) What is the velocity (in ft/s) afer 1 second?
v(1) =
ft/s
(c) When is the particle at rest? (Enter your answers as a comma-separated list.)
t =
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
(e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.
ft
(f) Find the acceleration (in ft/s?) at time t.
a(t) =
ft/s2
Find the acceleration (in ft/s²) after 1 second.
a(1) =
ft/s2
(g) Graph the position, velocity, and acceleration functions for 0 sts 6.
a
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