Only need Part D please. I have the answer of 14.13 but don't understand how to get it. For 0 ≤ t ≤ 6, a particle is moving along the x-axis. The particle's position, x(t), is not explicitly given.The velocity of the particle is given by v(t) = 2 sin(e¹/4) + 1. The acceleration of the particle is given by1a(t) = ¹⁄e¹/4 cos(e¹/4) and x(0) = 2.(a) Is the speed of the particle increasing or decreasing at time t = 5.5 ? Give a reason for your answer.(b) Find the average velocity of the particle for the time period 0 ≤ t ≤ 6.(c) Find the total distance traveled by the particle from time t = 0 to t = 6.(d) For 0 ≤ t ≤ 6, the particle changes direction exactly once. Find the position of the particle at that time.

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Answered: For 0 ≤ t ≤ 6, a particle is moving…

Math

Calculus

For 0 ≤ t ≤ 6, a particle is moving along the x-axis. The particle's position, x(t),

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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Only need Part D please. I have the answer of 14.13 but don't understand how to get it.

For 0 ≤ t ≤ 6, a particle is moving along the x-axis. The particle's position, x(t), is not explicitly given.
The velocity of the particle is given by v(t) = 2 sin(e¹/4) + 1. The acceleration of the particle is given by
1
a(t) = ¹⁄e¹/4 cos(e¹/4) and x(0) = 2.
(a) Is the speed of the particle increasing or decreasing at time t = 5.5 ? Give a reason for your answer.
(b) Find the average velocity of the particle for the time period 0 ≤ t ≤ 6.
(c) Find the total distance traveled by the particle from time t = 0 to t = 6.
(d) For 0 ≤ t ≤ 6, the particle changes direction exactly once. Find the position of the particle at that time.

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