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Problems
Mathematics
Mathematics
Problem
The velocity of a particle is given by
v
(
t
)
=
{
6
0
≤
t
<
2
−
3
t
+
12
2
≤
t
<
6
2
t
−
14
6
≤
t
≤
9
v(t)=\begin{cases} 6 & 0\le t<2 \\ -3t+12 & 2\le t<6 \\ 2t-14 & 6\le t\le 9 \end{cases}
v
(
t
)
=
⎩
⎨
⎧
6
−
3
t
+
12
2
t
−
14
0
≤
t
<
2
2
≤
t
<
6
6
≤
t
≤
9
, with
v
v
v
in meters per second and
t
t
t
in seconds. If the particle’s position is
s
(
0
)
=
0
s(0)=0
s
(
0
)
=
0
, determine its position
s
(
9
)
s(9)
s
(
9
)
at
t
=
9
s
t=9\text{ s}
t
=
9
s
.
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