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Mathematics
Mathematics
Problem
For
0
≤
t
≤
2
π
0\le t\le 2\pi
0
≤
t
≤
2
π
, a particle’s velocity is
v
(
t
)
=
sin
t
−
1
2
v(t)=\sin t-\dfrac12
v
(
t
)
=
sin
t
−
2
1
. At which times in the interval does the particle change direction? a)
t
=
π
6
t=\dfrac{\pi}{6}
t
=
6
π
only b)
t
=
π
6
and
t
=
5
π
6
t=\dfrac{\pi}{6}\text{ and }t=\dfrac{5\pi}{6}
t
=
6
π
and
t
=
6
5
π
c)
t
=
π
2
and
t
=
3
π
2
t=\dfrac{\pi}{2}\text{ and }t=\dfrac{3\pi}{2}
t
=
2
π
and
t
=
2
3
π
d)
t
=
π
6
,
t
=
5
π
6
,
and
t
=
3
π
2
t=\dfrac{\pi}{6},\; t=\dfrac{5\pi}{6},\text{ and } t=\dfrac{3\pi}{2}
t
=
6
π
,
t
=
6
5
π
,
and
t
=
2
3
π
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