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 ?

Explanation

When speed becomes constant acceleration `a = (dv)/(dt) =0`
`a = g - bv `(given)
It is clear from above equation as speed increases acceleration will decrease. At a certain speed say `v _(0),` acceleration will be zero and speed will remain constant.
`implies a = g - b v _(0)`
`therefore 0 =g - bv _(0)`
`therefore v _(0) = (g)/(b)`