A particle of mass m moves along a curve $y=x^2$ When particle has x- co-ordinate as 1/2 and x-component of velocity as 4 m/s then select the wrong Statement.

On the curve, $y=x^2;\text{ at }x=1/2,y=1/4$.

Hence the coordinate $(1/2,1/4)$

Differentiating : $y=x^2$

$v_y=2x{v}_x$

$v_y=2\left(\frac{1}{2}\right)\left(4\right)=4m/s$

Which satisfies the line $4x-4y-1=0$

(tangent to the curve)
and magnitude of velocity :

$\left|\overrightarrow{v}\right|=\sqrt{v_x^2+v_y^2}=4\sqrt{2}\mathrm{m}/\mathrm{s}$

As the line $4x-4y=1$ does not pass through the origin.