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Mathematics
Mathematics
Problem
The position of a bug crawling on a sheet is given by
r
(
t
)
=
⟨
sin
3
t
,
ln
(
t
2
+
1
)
⟩
r(t)=\langle \sin 3t,\;\ln(t^{2}+1)\rangle
r
(
t
)
=
⟨
sin
3
t
,
ln
(
t
2
+
1
)⟩
, with
t
t
t
in seconds and coordinates in centimeters. Find the velocity components at
t
=
0.5
s
t=0.5\text{ s}
t
=
0.5
s
, expressing each component exactly.
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