The motion of a body falling from rest in a viscous medium is described by \(\frac{dv}{dt} = A - Bv\), where A and B are constants. The velocity at time t is given by :
Solution:
Integrating the equation \(\int_0^v \frac{dv}{A - Bv} = \int_0^t dt\) gives \(-\frac{1}{B} \ln(\frac{A - Bv}{A}) = t\). Simplifying for velocity gives \(v = \frac{A}{B}(1 - e^{-Bt})\).
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