Ncert Exercises & Solutions

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?

Hint: When speed becomes constant, acceleration, a =

\frac{dv}{dt}

$\frac{dv}{dt}$ = 0.

$\begin{array}{l} Step 1 : Calculate speed by equating acceleration = 0 . \\ Given acceleration a = g - bv \end{array}$ $\begin{array}{l} Step 1 : Calculate speed by equating acceleration = 0 . \\ Given acceleration a = g - bv \end{array}$

Clearly, from the above equation as speed increases acceleration will decrease. At a certain speed say $V_{0}$ $V_{0}$ , acceleration will be zero and speed will remain constant.

$\begin{array}{lr} Hence, & a = g - {bv}_{0} = 0 \\ \Rightarrow & v_{0} = g / b \end{array}$ $\begin{array}{lr} Hence, & a = g - {bv}_{0} = 0 \\ \Rightarrow & v_{0} = g / b \end{array}$

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