The position of a particle after t seconds is given by s = (t + 1) ln(t + 1) − 2t, where s is measured in meters. Positive values of s indicate that the particle is east of its starting point, while negative values of s indicate that it is west of its starting point. (a) Find the exact time(s) when the velocity of the particle is zero. If its velocity is never zero, explain why. (b) Find the exact time(s) when the acceleration of the particle is zero. If its acceleration is never zero, explain why.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter2: Motion In One Dimension
Section: Chapter Questions
Problem 6P: The position of a particle moving along the x axis varies in time according to the expression x =...
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The position of a particle after t seconds is given by s = (t + 1) ln(t + 1) − 2t, where s is measured in meters. Positive values of s indicate that the particle is east of its starting point, while negative values of s indicate that it is west of its starting point.

(a) Find the exact time(s) when the velocity of the particle is zero. If its velocity is never zero, explain why.

(b) Find the exact time(s) when the acceleration of the particle is zero. If its acceleration is never zero, explain why.

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