If the velocity of a body moving in $a$straight line is proportional to the square root of the distance travelled, then it moves with

Let $v$ be the velocity and $s$ be the distance travelled

by the body at any time $t$. Then,

$\begin{array}{l} v\propto \sqrt{s}\\ \Rightarrow v=\lambda \sqrt{s},\end{array}$where $\lambda$ is a constant

$\begin{array}{l}\Rightarrow \frac{dv}{dt}=\frac{\lambda }{2\sqrt{s}}\frac{ds}{dt}\\ \Rightarrow \frac{dv}{dt}=\frac{\lambda }{2\sqrt{s}}\left(\lambda \sqrt{s}\right)=\frac{{\lambda }^2}{2}=\mathrm{const}.\end{array}$

$\Rightarrow$  Acceleration $=$Constant 

Hence, the body moves with constant force.