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Problem
Set 1: Problem 4.
Problem:
A particle’s position is given by
x
=
L
[(
t/
τ
)
3
−
3(
t/
τ
−
1)
2
]
,where
L
and
τ
are characteristic
length and time scales. Compute the time at which the acceleration is zero. What are the position and
velocity of the particle at this time?
Solution:
First, to simplify the differentiation process, rewrite the particle’s position as follows.
x
=
L
τ
3
J
t
3
−
3
τ
(
t
−
τ
)
2
o
The velocity of the particle is
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This note was uploaded on 10/12/2009 for the course AME 301 at USC.
 '06
 Shiflett

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