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Mathematics
Mathematics
Problem
For
t
>
0
t>0
t
>
0
, a particle moves with velocity
v
(
t
)
=
t
2
i
+
ln
(
t
)
j
+
4
cos
t
k
\mathbf v(t)=t^{2}\mathbf i+\ln(t)\,\mathbf j+4\cos t\,\mathbf k
v
(
t
)
=
t
2
i
+
ln
(
t
)
j
+
4
cos
t
k
. At time
t
=
1
t=1
t
=
1
its position is
r
(
1
)
=
⟨
2
,
0
,
5
⟩
\mathbf r(1)=\langle 2,0,5\rangle
r
(
1
)
=
⟨
2
,
0
,
5
⟩
. Derive an explicit expression for
r
(
t
)
\mathbf r(t)
r
(
t
)
.
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