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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line5 Marks
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?
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Answer

Key concept: If a spherical body of radius r is dropped in a viscous fluid, it is first accelerated and then its acceleration becomes zero and it attains a constant velocity called terminal velocity. According to the problem, acceleration of object is given by the relation a = g - bv When speed becomes constant acceleration $\text{a}=\frac{\text{dv}}{\text{dt}}=0$ (uniform motion). where, g = gravitational acceleration Clearly, 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. Hence, $\text{a}=\text{g}-\text{bv}_0=0$ $\Rightarrow\text{v}_0=\frac{\text{g}}{\text{b}}$

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