If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then itsacceleration is

A
a constant
B
$\propto s^{2}$
C
$\propto \frac{1}{s^{2}}$
D
$\propto s$

Solution:

Let $v$ be the velocity of the particle when the

distance covered is $s$ . Then,

$\begin{array}{l} v \propto \sqrt{s} [G i v e n] \\ \Rightarrow v = λ \sqrt{s} \\ \Rightarrow \frac{d v}{d s} = \frac{λ}{2 \sqrt{s}} \\ \Rightarrow v \frac{d v}{d s} = \frac{λ v}{2 \sqrt{s}} = \frac{λ^{2}}{2} = constant. \end{array}$

Hence, the acceleration is constant.

If a particle is moving such that the velocity acquired
is proportional to the square root of the distance covered, then its
acceleration is

Solution:

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