Q16 of 26 Page 16

An object falling through a fluid is observed to have acceleration given by a = g – bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?

The acceleration of the object in the fluid is a = g – bv.

We know that acceleration is the derivative of velocity with respect to time.




Integrating with proper limits





As t approaches infinity, the exponential factor reaches zero. Thus, the object has a constant speed of g/b.


Alternative Way:


After a long time of release, speed is constant (say v’) which implies there is no acceleration. Acceleration is given by



This implies, the constant speed v’= g/b.


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