3. A particle moves in space along a path whose parametric equations are given by x₁ = b sin wt, x₂ = b cos wt, x3 = c where b and care constants. a. Find its position at vector , velocity, and acceleration à at any time t. b. Show that the particle traverses its path with constant speed and that its distance from the origin remains constant. c. Show that the acceleration is perpendicular to the velocity and the x3-axis. d. Determine the trajectory of the particle, that is, the path described in terms of spatial coordinates only. Sketch the trajectory.
3. A particle moves in space along a path whose parametric equations are given by x₁ = b sin wt, x₂ = b cos wt, x3 = c where b and care constants. a. Find its position at vector , velocity, and acceleration à at any time t. b. Show that the particle traverses its path with constant speed and that its distance from the origin remains constant. c. Show that the acceleration is perpendicular to the velocity and the x3-axis. d. Determine the trajectory of the particle, that is, the path described in terms of spatial coordinates only. Sketch the trajectory.
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Transcribed Image Text:3.
A particle moves in space along a path whose parametric equations are given by
x₁ = b sin wt, x₂ = b cos wt, x3 = c
where b and care constants.
a.
Find its position at vector , velocity , and acceleration à at any time t.
b. Show that the particle traverses its path with constant speed and that its distance
from the origin remains constant.
Show that the acceleration is perpendicular to the velocity and the x3-axis.
Determine the trajectory of the particle, that is, the path described in terms of spatial
coordinates only. Sketch the trajectory.
c.
d.
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