Problem
Set 1: Problem 4.
Problem:
A particle’s position is given by
x
=
R
[2(
t/
τ
)
3
−
(
t/
τ
)
4
]
,whe
re
R
and
τ
are characteristic
length and time scales. Compute the time,
t>
0
, at which the velocity is zero. What are the position
and acceleration of the particle at this time?
Solution:
First, to simplify the differentiation process, rewrite the particle’s position as follows.
x
=
R
τ
4
J
2
τ
t
3
−
t
4
o
The velocity of the particle is
v
=
dx
dt
=
R
τ
4
J
6
τ
t
2
−
4
t
3
o
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 Spring '06
 Shiflett
 Velocity, Particle

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