A body's velocity varies with displacement 'x' as follows v² = ax². Here a is a constant. What is the body's acceleration?

Concept:  A body's velocity is the rate at which its displacement changes.

The magnitude and direction of velocity are both vector quantities in two dimensions.

Given that:

 v² = ax²

Differential both sides with respect to x,

2v$\left(\frac{dv}{dx}\right)$= 2ax

$v\left(\frac{dv}{dx}\right)=ax$

Since $a=\frac{dv}{dt}$, and Velocity $v=\frac{dx}{dt}$ 

Now $a=\frac{dv}{dt}$

             $=\frac{dv}{dx}\times \frac{dx}{dt}$

              $=v\frac{dv}{dx}$

Hence acceleration $a=v\frac{dv}{dx}$=$ax$ 

 Since a is constant, acceleration will be a variable that changes with displacement x and hence it is non-uniform acceleration.