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Mathematics
Mathematics
Problem
For a particle with acceleration
a
(
t
)
=
⟨
6
t
,
3
⟩
\mathbf a(t)=\langle 6t,3\rangle
a
(
t
)
=
⟨
6
t
,
3
⟩
, the velocity at time
t
=
2
t=2
t
=
2
is
v
(
2
)
=
⟨
5
,
−
1
⟩
\mathbf v(2)=\langle 5,-1\rangle
v
(
2
)
=
⟨
5
,
−
1
⟩
and the position at time
t
=
0
t=0
t
=
0
is
r
(
0
)
=
⟨
0
,
4
⟩
\mathbf r(0)=\langle 0,4\rangle
r
(
0
)
=
⟨
0
,
4
⟩
. Find an explicit formula for the position vector
r
(
t
)
\mathbf r(t)
r
(
t
)
.
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