The given graph shows the variation of velocity (v) with displacement $\left(x\right)$ . Which one of the following graph correctly represents the variation of acceleration (a) with displacement?

Given graph is a straight line with equation  $v=v_0-\frac{v_0}{x_0}x.$
Differentiate the velocity  $v$ w.r.t. time  $t$ to get the acceleration
$a=\frac{\text{d}v}{\text{d}t}=\frac{\text{d}v}{\text{d}x}\frac{\text{d}x}{\text{d}t}=v\frac{\text{d}v}{\text{d}x}$
$=-\frac{v_0}{x_0}(v_0-\frac{v_0}{x_0}x)=-\frac{v_0^2}{x_0}+\frac{v_0^2}{x_0^2}x.$
Thus, a‐x graph is a straight line with negative intercept on $\alpha$  axis and a positive slope.