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

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

Calculus: Early Transcendentals
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.
Transcribed Image Text: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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