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Mathematics
Mathematics
Problem
A particle moves in the plane so that
d
x
d
t
=
2
t
\dfrac{dx}{dt}=2t
d
t
d
x
=
2
t
and
d
y
d
t
=
3
t
2
\dfrac{dy}{dt}=3t^{2}
d
t
d
y
=
3
t
2
. At time
t
=
0
t=0
t
=
0
the particle is located at the point
(
1
,
−
2
)
(1,-2)
(
1
,
−
2
)
. Which of the following is the correct expression for
y
y
y
as a function of
t
t
t
? a)
3
t
3
−
2
3t^{3}-2
3
t
3
−
2
b)
t
3
−
2
t^{3}-2
t
3
−
2
c)
t
3
+
1
t^{3}+1
t
3
+
1
d)
t
3
+
2
t^{3}+2
t
3
+
2
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