An object falling through a fluid is having acceleration given by a = g – bv where b and g are positive constants and v is instantaneous velocity. The time at which velocity becomes half of maximum velocity is (initial velocity of the object is zero)
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Explanation:
first integrate dv /dt = g - bv and don't forgot constant of integration. Use origin as the initial condition to solve Integral and find v in terms of time eventually.
Now a = 0 , gives you condition of terminal velocity ( v$_t$ ) or so called maximum velocity.
Now t = t' , when v = v$_t$ /2 , it gives you value of t' when velocity becomes half of maximum velocity.
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