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Mathematics
Problem
A particle moves along a straight line with continuous velocity
v
(
t
)
v(t)
v
(
t
)
. If its position at time
t
=
0
t=0
t
=
0
is
3
3
3
, which of the following expressions gives its position
s
(
T
)
s(T)
s
(
T
)
for any
T
>
0
T>0
T
>
0
? a)
3
+
∫
0
T
∣
v
(
t
)
∣
d
t
3+\int_{0}^{T} |v(t)|\,dt
3
+
∫
0
T
∣
v
(
t
)
∣
d
t
b)
3
+
∫
0
T
v
(
t
)
d
t
3+\int_{0}^{T} v(t)\,dt
3
+
∫
0
T
v
(
t
)
d
t
c)
∫
0
T
v
(
t
)
d
t
\displaystyle \int_{0}^{T} v(t)\,dt
∫
0
T
v
(
t
)
d
t
d)
3
+
T
v
(
T
)
3+T\,v(T)
3
+
T
v
(
T
)
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