A particle moves along the x axis. It is initially at the position 0.270 m, moving with velocity 0.230 m/s and acceleration -0.340 m/s2. Suppose it moves with constant acceleration for 4.20 s. (a) Find the position of the particle after this time. -1.76 m (b) Find its velocity at the end of this time interval. -1.19 m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 4.20 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. m (e) Find its phase constant Po if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. rad (f) Find its position after it oscillates for 4.20 s. m (g) Find its velocity at the end of this 4.20 s time interval. m/s
A particle moves along the x axis. It is initially at the position 0.270 m, moving with velocity 0.230 m/s and acceleration -0.340 m/s2. Suppose it moves with constant acceleration for 4.20 s. (a) Find the position of the particle after this time. -1.76 m (b) Find its velocity at the end of this time interval. -1.19 m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 4.20 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. m (e) Find its phase constant Po if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. rad (f) Find its position after it oscillates for 4.20 s. m (g) Find its velocity at the end of this 4.20 s time interval. m/s
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 7CQ
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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.
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Transcribed Image Text:A particle moves along the x axis. It is initially at the position 0.270 m, moving with velocity 0.230 m/s and acceleration
-0.340 m/s2. Suppose it moves with constant acceleration for 4.20 s.
(a) Find the position of the particle after this time.
|-1.76
(b) Find its velocity at the end of this time interval.
-1.19
m/s
We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it
oscillates in simple harmonic motion for 4.20 s around the equilibrium position x = 0. Hint: the following problems are very
sensitive to rounding, and you should keep all digits in your calculator.
(c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x.
/s
(d) Find the amplitude of the oscillation. Hint: use conservation of energy.
m
(e) Find its phase constant Po if cosine is used for the equation of motion. Hint: when taking the inverse of a trig
function, there are always two angles but your calculator will tell you only one and you must decide which of the two
angles you need.
rad
(f) Find its position after it oscillates for 4.20 s.
(g) Find its velocity at the end of this 4.20 s time interval.
m/s
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