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.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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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