Solution Found!
Section 4.2 Two-Dimensional KinematicsA particle’s
Chapter 4, Problem 8E(choose chapter or problem)
A particle's trajectory is described by \(x=\left(\frac{1}{2} t^{3}-2 t^{2}\right) \mathrm{m}\) and \(y=\left(\frac{1}{2} t^{2}-2 t\right) \mathrm{m}\), where \(t\) is in s.
a. What are the particle's position and speed at \(t=0 \mathrm{~s}\) and \(t=4 \mathrm{~s}\)?
b. What is the particle's direction of motion, measured as an angle from the \(x\)-axis, at \(t=0 \mathrm{~s}\) and \(t=4 \mathrm{~s}\)?
Equation Transcription:
)m
Text Transcription:
x=(1/2 t^3-2 t^2)m
y=(1/2 t^2-2t)m
t
t=0 s
t= 4 s
x-axis
t=0 s
t= 4 s
Questions & Answers
QUESTION:
A particle's trajectory is described by \(x=\left(\frac{1}{2} t^{3}-2 t^{2}\right) \mathrm{m}\) and \(y=\left(\frac{1}{2} t^{2}-2 t\right) \mathrm{m}\), where \(t\) is in s.
a. What are the particle's position and speed at \(t=0 \mathrm{~s}\) and \(t=4 \mathrm{~s}\)?
b. What is the particle's direction of motion, measured as an angle from the \(x\)-axis, at \(t=0 \mathrm{~s}\) and \(t=4 \mathrm{~s}\)?
Equation Transcription:
)m
Text Transcription:
x=(1/2 t^3-2 t^2)m
y=(1/2 t^2-2t)m
t
t=0 s
t= 4 s
x-axis
t=0 s
t= 4 s
ANSWER:
Step 1 of 4
The objective here is to determine:
(A) The position and speed of a particle at \(t=0 \mathrm{~s}\) and \(t=4 \mathrm{~s}\) from the given position coordinates.
(B) The direction of motion of the particle in terms of the angle measured from the \(x\)-axis.
Part (a)