Question

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

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

Answer 1

The correct option is A a constant

Given, velocity $v\propto \sqrt{s}$

$\Rightarrow v=k\sqrt{s}$

$\frac{dv}{dt}=\frac{k}{2\sqrt{s}}\frac{ds}{dt}$

$\Rightarrow a=\frac{k^2}{2}$

Hence, acceleration is constant.