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Mathematics
Mathematics
Problem
A particle moves in the plane with acceleration
a
(
t
)
=
⟨
2
t
,
−
e
t
⟩
\mathbf a(t)=\langle 2t,-e^{t}\rangle
a
(
t
)
=
⟨
2
t
,
−
e
t
⟩
. Its velocity and position at time
t
=
0
t=0
t
=
0
are
v
(
0
)
=
⟨
1
,
0
⟩
\mathbf v(0)=\langle 1,0\rangle
v
(
0
)
=
⟨
1
,
0
⟩
and
r
(
0
)
=
⟨
2
,
−
3
⟩
\mathbf r(0)=\langle 2,-3\rangle
r
(
0
)
=
⟨
2
,
−
3
⟩
, respectively. Determine the particle’s position vector at time
t
=
2
t=2
t
=
2
.
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