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Physics
Physics
Problem
Which of the following expressions gives the total work
W
W
W
done on a system between
t
=
0
t=0
t
=
0
and
t
=
T
t=T
t
=
T
in terms of its power output
P
(
t
)
P(t)
P
(
t
)
? a)
W
=
∫
0
T
P
(
t
)
d
t
W=\displaystyle\int_0^T P(t)\,dt
W
=
∫
0
T
P
(
t
)
d
t
b)
W
=
1
T
∫
0
T
P
(
t
)
d
t
W=\dfrac{1}{T}\displaystyle\int_0^T P(t)\,dt
W
=
T
1
∫
0
T
P
(
t
)
d
t
c)
W
=
∫
0
T
d
P
d
t
d
t
W=\displaystyle\int_0^T \dfrac{dP}{dt}\,dt
W
=
∫
0
T
d
t
d
P
d
t
d)
W
=
P
(
T
)
T
W=P(T)\,T
W
=
P
(
T
)
T
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