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Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of v(t) = 8 √t - 4 m/s, where t is measured in seconds. Positive values of v indicate that the particle is moving to the east, while negative values of v indicate that it is moving to the west. (a) Does the particle ever reverse its direction? If so, at what time(s)? V 1 v(t) dt, and give your answer as a decimal approximation. Then, use a complete sentence (b) Calculate to explain the meaning of your answer in the context of this problem. (c) Find the total distance traveled by the particle on the time interval 1 ≤ t ≤ 6. Include units, and circle your answer.

Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of v(t) = 8 √t - 4 m/s, where t is measured in seconds. Positive values of v indicate that the particle is moving to the east, while negative values of v indicate that it is moving to the west. (a) Does the particle ever reverse its direction? If so, at what time(s)? V 1 v(t) dt, and give your answer as a decimal approximation. Then, use a complete sentence (b) Calculate to explain the meaning of your answer in the context of this problem. (c) Find the total distance traveled by the particle on the time interval 1 ≤ t ≤ 6. Include units, and circle your answer.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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5. Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of v(t) = 8 √t m/s, where t is measured in seconds. Positive values of v indicate that the particle is moving to the east, while negative values of v indicate that it is moving to the west. (a) Does the particle ever reverse its direction? If so, at what time(s)? 1 6 6 v(t) dt, and give your answer as a decimal approximation. Then, use a complete sentence (b) Calculate to explain the meaning of your answer in the context of this problem. (c) Find the total distance traveled by the particle on the time interval 1 ≤ t ≤ 6. Include units, and circle your answer.
Transcribed Image Text:5. Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of v(t) = 8 √t m/s, where t is measured in seconds. Positive values of v indicate that the particle is moving to the east, while negative values of v indicate that it is moving to the west. (a) Does the particle ever reverse its direction? If so, at what time(s)? 1 6 6 v(t) dt, and give your answer as a decimal approximation. Then, use a complete sentence (b) Calculate to explain the meaning of your answer in the context of this problem. (c) Find the total distance traveled by the particle on the time interval 1 ≤ t ≤ 6. Include units, and circle your answer.
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