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Nov 2003 p3 q9
2285
Compressed air is escaping from a container. The pressure of the air in the container at time t is P, and the constant atmospheric pressure of the air outside the container is A. The rate of decrease of P is proportional to the square root of the pressure difference \\(P - A\\). Thus the differential equation connecting P and t is
\\(\frac{dP}{dt} = -k \sqrt{P - A} \\),
where k is a positive constant.
- Find, in any form, the general solution of this differential equation. [3]
- Given that P = 5A when t = 0, and that P = 2A when t = 2, show that k = \\(\sqrt{A} \\). [4]
- Find the value of t when P = A. [2]
- Obtain an expression for P in terms of A and t. [2]
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