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Mathematics
Problem
A path is traced in two consecutive time intervals. Segment 1 (
0
≤
t
≤
1
0\le t\le 1
0
≤
t
≤
1
):
r
1
(
t
)
=
⟨
3
t
,
4
t
⟩
\mathbf r_1(t)=\langle 3t,\,4t\rangle
r
1
(
t
)
=
⟨
3
t
,
4
t
⟩
Segment 2 (
1
<
t
≤
2
1< t\le 2
1
<
t
≤
2
):
r
2
(
t
)
=
⟨
3
+
(
t
−
1
)
2
,
4
+
2
(
t
−
1
)
⟩
\mathbf r_2(t)=\langle 3+(t-1)^2,\,4+2(t-1)\rangle
r
2
(
t
)
=
⟨
3
+
(
t
−
1
)
2
,
4
+
2
(
t
−
1
)⟩
Compute the total length of the entire path from
t
=
0
t=0
t
=
0
to
t
=
2
t=2
t
=
2
.
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