A particle moves according to a law of motion s = (t), 0 sts 12, where t is measured in seconds and s in feet. Rt) = cos(Tt/6) (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity after 1 s? (Round your answer to two decimal places.) v(1) = t/s (c) When is the particle at rest? |s (smallest value) ]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. (1) Find the acceleration at time t (in frt/s). a(t) = Find the acceleration after 1 s. (Round your answer to two decimal places.) a(1) = (9) Graph the position, velocity, and acceleration functions for 0 sts 12. y y 1.0 1.0 0.5 0.5 4 6. 12 4 6. -0.5 -0.5 -1.0 -1.0 y y 1.0 1.0 0.5 0.5 6. 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 = (t), 0 sts 12, where t is measured in seconds and s in feet. Rt) = cos(Tt/6) (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity after 1 s? (Round your answer to two decimal places.) v(1) = t/s (c) When is the particle at rest? |s (smallest value) ]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. (1) Find the acceleration at time t (in frt/s). a(t) = Find the acceleration after 1 s. (Round your answer to two decimal places.) a(1) = (9) Graph the position, velocity, and acceleration functions for 0 sts 12. y y 1.0 1.0 0.5 0.5 4 6. 12 4 6. -0.5 -0.5 -1.0 -1.0 y y 1.0 1.0 0.5 0.5 6. 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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
Related questions
Question
![A particle moves according to a law of motion s = (t), 0 sts 12, where t is measured in seconds and s in feet.
Rt) = cos(Tt/6)
(a) Find the velocity at time t (in ft/s).
v(t) =
(b) What is the velocity after 1 s? (Round your answer to two decimal places.)
v(1) =
t/s
(c) When is the particle at rest?
|s (smallest value)
]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.
(1) Find the acceleration at time t (in frt/s).
a(t) =
Find the acceleration after 1 s. (Round your answer to two decimal places.)
a(1) =
(9) Graph the position, velocity, and acceleration functions for 0 sts 12.
y
y
1.0
1.0
0.5
0.5
4
6.
12
4
6.
-0.5
-0.5
-1.0
-1.0
y
y
1.0
1.0
0.5
0.5
6.
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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2f56214-094b-40bc-9658-0f1954b4c25b%2Fe5465cf9-48a9-44f7-8ab2-41e18fffee85%2F5dg5932_processed.png&w=3840&q=75)
Transcribed Image Text:A particle moves according to a law of motion s = (t), 0 sts 12, where t is measured in seconds and s in feet.
Rt) = cos(Tt/6)
(a) Find the velocity at time t (in ft/s).
v(t) =
(b) What is the velocity after 1 s? (Round your answer to two decimal places.)
v(1) =
t/s
(c) When is the particle at rest?
|s (smallest value)
]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.
(1) Find the acceleration at time t (in frt/s).
a(t) =
Find the acceleration after 1 s. (Round your answer to two decimal places.)
a(1) =
(9) Graph the position, velocity, and acceleration functions for 0 sts 12.
y
y
1.0
1.0
0.5
0.5
4
6.
12
4
6.
-0.5
-0.5
-1.0
-1.0
y
y
1.0
1.0
0.5
0.5
6.
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.)
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