can you helped solve these three steps because I am having a difficult time trying to figure out this problem, can you show the parts and can you please solve this problem step by step so I can understand better and follow along The position of a particle after \( t \) seconds is given by \( \mathbf{r}(t) = \langle t^2, 4t, 4\ln t \rangle \) for \( t \geq 1 \).(a) Calculate the position, velocity, and acceleration of the particle when \( t = 2 \).(b) Calculate the total distance traveled by the particle from \( t = 1 \) to \( t = e^2 \).(c) Is the object speeding up or slowing down at \( t = e^2 \) seconds?

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The position of a particle after t seconds is given by r(t) = (t2,4t, 4 ln t) for t > 1. a) Calculate the position, velocity, and acceleration of the particle when t = 2. b) Calculate the total distance traveled by the particle from t = 1 to t = e². c) Is the object speeding up or slowing down at t = e² seconds?

The position of a particle after t seconds is given by r(t) = (t2,4t, 4 ln t) for t > 1. a) Calculate the position, velocity, and acceleration of the particle when t = 2. b) Calculate the total distance traveled by the particle from t = 1 to t = e². c) Is the object speeding up or slowing down at t = e² seconds?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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can you helped solve these three steps because I am having a difficult time trying to figure out this problem, can you show the parts and can you please solve this problem step by step so I can understand better and follow along

The position of a particle after \( t \) seconds is given by \( \mathbf{r}(t) = \langle t^2, 4t, 4\ln t \rangle \) for \( t \geq 1 \).

(a) Calculate the position, velocity, and acceleration of the particle when \( t = 2 \).

(b) Calculate the total distance traveled by the particle from \( t = 1 \) to \( t = e^2 \).

(c) Is the object speeding up or slowing down at \( t = e^2 \) seconds?

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