2. Graphing Calculator allowed: A particle moves along a straight line. For 0 ≤ts 5, the velocity of the particle is given by v(t) = −2+ (t² + 3t) 6/5 - t³, and the position of the particle is given by s(t). It is known that s(0) = 10. a) Find all values of t in the interval 2 ≤ t≤ 4 for which the speed of the particle is 2. b) Write an expression involving an integral that gives the position s(t). Use this expression to find the position of the particle at time t = 5. c) Find all times t in the interval 0 ≤t ≤ 5 at which the particle changes direction. Justify your answer. d) Is the speed of the particle increasing or decreasing at time t = 4? Give a reason for your answer.
2. Graphing Calculator allowed: A particle moves along a straight line. For 0 ≤ts 5, the velocity of the particle is given by v(t) = −2+ (t² + 3t) 6/5 - t³, and the position of the particle is given by s(t). It is known that s(0) = 10. a) Find all values of t in the interval 2 ≤ t≤ 4 for which the speed of the particle is 2. b) Write an expression involving an integral that gives the position s(t). Use this expression to find the position of the particle at time t = 5. c) Find all times t in the interval 0 ≤t ≤ 5 at which the particle changes direction. Justify your answer. d) Is the speed of the particle increasing or decreasing at time t = 4? Give a reason for your answer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
Question
![2. Graphing Calculator allowed: A particle moves along a straight line. For 0 ≤ts
5, the velocity of the particle is given by v(t) = −2+ (t² + 3t) 6/5 - t³, and the
position of the particle is given by s(t). It is known that s(0) = 10.
a) Find all values of t in the interval 2 ≤ t≤ 4 for which the speed of the
particle is 2.
b) Write an expression involving an integral that gives the position s(t).
Use this expression to find the position of the particle at time t = 5.
c) Find all times t in the interval 0 ≤t ≤ 5 at which the particle changes
direction. Justify your answer.
d) Is the speed of the particle increasing or decreasing at time t = 4? Give
a reason for your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15abed78-e0e9-4b0e-bd06-c478a91e60f6%2F56d87212-5c97-466f-9a93-81b22e90a39f%2F2hzg1tj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Graphing Calculator allowed: A particle moves along a straight line. For 0 ≤ts
5, the velocity of the particle is given by v(t) = −2+ (t² + 3t) 6/5 - t³, and the
position of the particle is given by s(t). It is known that s(0) = 10.
a) Find all values of t in the interval 2 ≤ t≤ 4 for which the speed of the
particle is 2.
b) Write an expression involving an integral that gives the position s(t).
Use this expression to find the position of the particle at time t = 5.
c) Find all times t in the interval 0 ≤t ≤ 5 at which the particle changes
direction. Justify your answer.
d) Is the speed of the particle increasing or decreasing at time t = 4? Give
a reason for your answer.
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