A particle moves along the x axis. It is initially at the position 0.340 m, moving with velocity 0.100 m/s and acceleration -0.410 m/s2. Suppose it moves with constant acceleration for 3.60 s. (a) Find the position of the particle after this time. -1.95 (b) Find its velocity at the end of this time interval. -1.38 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 3.60 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. 1.09 V /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. .35 (e) Find its phase constant o, 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. -.26 rad (f) Find its position after it oscillates for 3.60 s. (g) Find its velocity at the end of this 3.60 s time interval. .2 m/s

A particle moves along the x axis. It is initially at the position 0.340 m, moving with velocity 0.100 m/s and acceleration -0.410 m/s2. Suppose it moves with constant acceleration for 3.60 s. (a) Find the position of the particle after this time. -1.95 (b) Find its velocity at the end of this time interval. -1.38 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 3.60 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. 1.09 V /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. .35 (e) Find its phase constant o, 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. -.26 rad (f) Find its position after it oscillates for 3.60 s. (g) Find its velocity at the end of this 3.60 s time interval. .2 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 20P

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