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Mathematics
Mathematics
Problem
The position of a particle is
s
(
t
)
=
t
3
−
6
k
t
2
+
9
k
2
t
s(t)=t^{3}-6kt^{2}+9k^{2}t
s
(
t
)
=
t
3
−
6
k
t
2
+
9
k
2
t
, where
k
k
k
is a positive constant and
t
t
t
is in seconds. The particle attains a local maximum position at
t
=
2
s
t=2\text{ s}
t
=
2
s
. What is the value of
k
k
k
? a)
k
=
2
3
k=\dfrac{2}{3}
k
=
3
2
b)
k
=
1
k=1
k
=
1
c)
k
=
2
k=2
k
=
2
d)
k
=
4
k=4
k
=
4
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