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Question
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?
Solution
When speed becomes constant acceleration a = `(dv)/(dt)` = 0
Given acceleration a = g – bv
Where, g = gravitational acceleration
Clearly, from the above equation as speed increases acceleration will decrease. At a certain speed say v0, acceleration will be zero and speed will remain constant.
Hence, a = g – bv0 = 0
⇒ v0 = g/b
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