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Mathematics
Mathematics
Problem
A particle moves in space with position vector
r
(
t
)
=
⟨
t
3
−
3
t
,
t
2
,
2
t
⟩
\mathbf r(t)=\langle t^{3}-3t,\,t^{2},\,2t\rangle
r
(
t
)
=
⟨
t
3
−
3
t
,
t
2
,
2
t
⟩
for
t
≥
0
t\ge 0
t
≥
0
. (a) Determine all times
t
t
t
when the velocity and acceleration vectors are orthogonal. (b) At
t
=
2
t=2
t
=
2
, state whether the particle’s speed is increasing or decreasing.
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