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Mathematics
Mathematics
Problem
For
t
≥
0
t\ge 0
t
≥
0
, a particle has velocity
v
(
t
)
=
⟨
2
sin
t
+
1
,
3
t
2
⟩
\mathbf v(t)=\langle 2\sin t+1,\;3t^{2}\rangle
v
(
t
)
=
⟨
2
sin
t
+
1
,
3
t
2
⟩
meters per second. The particle’s
x
x
x
–coordinate is
4
4
4
meters at
t
=
0
t=0
t
=
0
, and its
y
y
y
–coordinate is
15
15
15
meters at
t
=
2
t=2
t
=
2
. Determine the particle’s position vector
r
(
2
)
\mathbf r(2)
r
(
2
)
, expressing each component exactly.
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