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

constant force

Let v be the velocity and s be the distance traversed by the body at any time t. Then,

$v \propto \sqrt{s}$

$\Rightarrow v=\lambda \sqrt{s}$, where $\lambda$ is a constant

$\Rightarrow \frac{d v}{d t}=\frac{\lambda}{2 \sqrt{s}} \frac{d s}{d t}$

$\Rightarrow \frac{d v}{d t}=\frac{\lambda}{2 \sqrt{s}}(\lambda \sqrt{s})=\frac{\lambda^2}{2}$ = const. 

⇒ Acceleration = Constant

Hence, the body moves with constant force.