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Joint Entrance Examination
Mathematics
Differential Equations
Question 315
Question 315 of 490
Medium
MCQ
V
(
t
)
V(t)
V
(
t
)
depreciates per
d
V
d
t
=
−
k
(
T
−
t
)
\dfrac{dV}{dt}=-k(T-t)
d
t
d
V
=
−
k
(
T
−
t
)
,
k
>
0
k>0
k
>
0
. The scrap value
V
(
T
)
V(T)
V
(
T
)
is (with
V
(
0
)
=
I
V(0)=I
V
(
0
)
=
I
):
A
I
−
k
T
2
2
I-\dfrac{kT^2}{2}
I
−
2
k
T
2
B
I
−
k
(
T
−
t
)
2
2
I-\dfrac{k(T-t)^2}{2}
I
−
2
k
(
T
−
t
)
2
C
e
−
k
T
e^{-kT}
e
−
k
T
D
T
2
−
1
k
T^2-\dfrac1k
T
2
−
k
1
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Official solution
Integrating:
V
(
t
)
=
I
+
k
2
(
t
2
−
2
t
T
)
V(t)=I+\dfrac k2(t^2-2tT)
V
(
t
)
=
I
+
2
k
(
t
2
−
2
tT
)
(using
V
(
0
)
=
I
V(0)=I
V
(
0
)
=
I
). At
t
=
T
t=T
t
=
T
:
V
(
T
)
=
I
−
k
T
2
2
V(T)=I-\dfrac{kT^2}{2}
V
(
T
)
=
I
−
2
k
T
2
.
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