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Mathematics
Mathematics
Problem
A particle moves so that
r
(
t
)
=
⟨
e
t
−
t
,
1
3
t
3
−
2
t
⟩
\mathbf r(t)=\langle e^{t}-t,\;\tfrac{1}{3}t^{3}-2t\rangle
r
(
t
)
=
⟨
e
t
−
t
,
3
1
t
3
−
2
t
⟩
for
0
≤
t
≤
3
0\le t\le3
0
≤
t
≤
3
. Determine all values of
t
t
t
in this interval where the particle is momentarily at rest, and state whether each corresponds to a change in the particle’s overall direction of motion.
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