A particle moves according to a law of motion s = f(t), 0 sts 12, where t is measured in seconds and s in feet. f(t) = cos(xt/6) (a) Find the velocity at time t (in ft/s). T sin v(t) = 6 (b) What is the velocity after 5 s? (Round your answer to two decimal places.) v(5) = [-0.26 ft/s (c) When is the particle at rest? s (smallest value) t = 16 12 s (largest value) (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 12 s. Ex ft Enter an exact number. (f) Find the acceleration at time t (in ft/s). a(t) = 6 36 Find the acceleration after 5 s. (Round your answer to two decimal places.) a(5) = 0.24 v ft/s? (g) Graph the position, velocity, and acceleration functions for 0 sts 12. y y 1.0 1.0 0.5 0.5 4 6 8 12 4 6. 8 -0.5 -0.5 -1.0 -1.0 y y 1.0 1.0 0,5 0.5 6. 8 4 6 -0.5 -0.5 -1.0 -1.0 (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.)
A particle moves according to a law of motion s = f(t), 0 sts 12, where t is measured in seconds and s in feet. f(t) = cos(xt/6) (a) Find the velocity at time t (in ft/s). T sin v(t) = 6 (b) What is the velocity after 5 s? (Round your answer to two decimal places.) v(5) = [-0.26 ft/s (c) When is the particle at rest? s (smallest value) t = 16 12 s (largest value) (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 12 s. Ex ft Enter an exact number. (f) Find the acceleration at time t (in ft/s). a(t) = 6 36 Find the acceleration after 5 s. (Round your answer to two decimal places.) a(5) = 0.24 v ft/s? (g) Graph the position, velocity, and acceleration functions for 0 sts 12. y y 1.0 1.0 0.5 0.5 4 6 8 12 4 6. 8 -0.5 -0.5 -1.0 -1.0 y y 1.0 1.0 0,5 0.5 6. 8 4 6 -0.5 -0.5 -1.0 -1.0 (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.)
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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Transcribed Image Text:A particle moves according to a law of motion s = f(t), 0 <ts 12, where t is measured in seconds and s in feet.
f(t) = cos(xt/6)
(a) Find the velocity at time t (in ft/s).
T sin T
v(t) =
6
(b) What is the velocity after 5 s? (Round your answer to two decimal places.)
v(5) = [-0.26
v ft/s
(c) When is the particle at rest?
t = [0
v s (smallest value)
t = 16
t = [12
V s (largest value)
(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 12 s.
EX ft
Enter an exact number.
(f) Find the acceleration at time t (in ft/s).
a(t) =
36
Find the acceleration after 5 s. (Round your answer to two decimal places.)
a(5) = (0.24
v ft/s?
(g) Graph the position, velocity, and acceleration functions for 0sts 12.
y
y
1.0
1.0
a
0.5
0.5
6
8
12
6
12
-0.5
-0.5
-1.0
-1.0
y
y
1.0
1.0
0.5F
0.5
a
6
8
12
6
8
12
-0.5
-0.5
-1.0
-1.0
(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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