A particle is moving in $xy$-plane crosses the origin at time $t=0.$ The equation of motion of the particle is $y=4x^2.$ If the velocity of the particle is $\overrightarrow{v}=(2\hat{\mathrm{i}}+2\hat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$ and acceleration is $\overrightarrow{a}=\left(a\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-2}$, then the magnitude of $a$ is