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Mathematics
Mathematics
Problem
A particle moves in the plane with velocity
v
(
t
)
=
⟨
3
t
2
,
−
2
⟩
\mathbf v(t)=\langle 3t^{2},-2\rangle
v
(
t
)
=
⟨
3
t
2
,
−
2
⟩
. Given that its position at
t
=
1
t=1
t
=
1
is
r
(
1
)
=
⟨
4
,
5
⟩
\mathbf r(1)=\langle 4,5\rangle
r
(
1
)
=
⟨
4
,
5
⟩
, determine the position vector
r
(
t
)
\mathbf r(t)
r
(
t
)
for all
t
t
t
.
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