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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. (b) Find its velocity at the end of this 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. (b) Find its velocity at the end of this time interval. m/s

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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. [______] m (b) Find its velocity at the end of this time interval. [______] 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 ϕ₀ 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
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. [______] m (b) Find its velocity at the end of this time interval. [______] 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 ϕ₀ 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
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