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Mathematics
Mathematics
Problem
A piston experiences a constant force of
F
=
1500
N
F=1500\,\text{N}
F
=
1500
N
. Its instantaneous area is
A
(
t
)
A(t)
A
(
t
)
cm
2
^{2}
2
, so the pressure is
P
(
t
)
=
F
A
(
t
)
P(t)=\dfrac{F}{A(t)}
P
(
t
)
=
A
(
t
)
F
. When
A
=
25
cm
2
A=25\,\text{cm}^{2}
A
=
25
cm
2
and
d
A
d
t
=
−
2
cm
2
/
s
\dfrac{dA}{dt}=-2\,\text{cm}^{2}/\text{s}
d
t
d
A
=
−
2
cm
2
/
s
, determine
d
P
d
t
\dfrac{dP}{dt}
d
t
d
P
in pascals per second
(
1
N/cm
2
=
10
4
Pa
)
(1\,\text{N/cm}^{2}=10^{4}\,\text{Pa})
(
1
N/cm
2
=
1
0
4
Pa
)
.
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