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A particle moves along the x-axis so that its velocity v at time t, for 0

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter4: Two-and-three Dimensional Motion

Section: Chapter Questions

Problem 59PQ: A particle has a nonzero acceleration and a nonzero constant speed at all times. What is the angle...

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Concept explainers

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.

Topic Video

Question

A particle moves along the x-axis so that its velocity v at time t, for 0 <t< 6, is given by:
v (t) = 4 sin
2t + 2
2
|
At time t = 0, the particle is at x=1.
(a) Find the velocity and acceleration of the particle at time t = 4.
(b) Is the speed of the particle increasing or decreasing at time t = 4? Give a reason for your
e Find the time when the particle first changes direction. Justify your reasoning.
(d) Describe the movement of the particle before, at, and after t = 2.

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