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Mathematics
Mathematics
Problem
A particle has velocity
v
(
t
)
=
⟨
e
2
t
,
2
e
2
t
,
3
⟩
\mathbf v(t)=\langle e^{2t},\,2e^{2t},\,3\rangle
v
(
t
)
=
⟨
e
2
t
,
2
e
2
t
,
3
⟩
and acceleration
a
(
t
)
=
⟨
2
e
2
t
,
4
e
2
t
,
0
⟩
\mathbf a(t)=\langle 2e^{2t},\,4e^{2t},\,0\rangle
a
(
t
)
=
⟨
2
e
2
t
,
4
e
2
t
,
0
⟩
. Determine whether the particle’s speed is increasing, decreasing, or constant at
t
=
0
t=0
t
=
0
.
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