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A body is in straight line motion with an acceleration given by a=32-4v . The initial conditions are at t=0 , v=4 . Find the velocity when t=ln2.
dv/(32-4v) = dt..
integrate
lhs from 4 to v
rhs from 0 to ln2
thus
-4ln(32-4v)]v,4 = ln2
32-4v]v,4 = 2^(-1/4)
32-4v -32 + 16 = 0.85
4v = 15approx
v = 3.7
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