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2.Motion in Straight Line
hard
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 ?
Option A
Option B
Option C
Option D
Solution
When speed becomes constant acceleration $a=\frac{d v}{d t}=0$
$a=g-b v$ (given)
It is clear from above equation as speed increases acceleration will decrease. At a certain speed
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say $\mathrm{v}_{0}$, acceleration will be zero and speed will remain constant.
$\Rightarrow a=g-b v_{0}$
$\therefore 0=\mathrm{g}-b v_{0}$
$\therefore v_{0}=\frac{g}{b}$
Standard 11
Physics
