JEE Main 2026 Apr 2 Shift 1, Physics Q3: Motion In Two And Three Dimension

Differentiate each component of $\vec{v}$ with respect to time, recognising that $\dot{x}=v_x=-x$, $\dot{y}=v_y=2y$, $\dot{z}=v_z=-z$:

$\vec{a}=-\dot{x}\hat{i}+2\dot{y}\hat{j}-\dot{z}\hat{k}=x\hat{i}+4y\hat{j}+z\hat{k}$

At $(1,2,4)$: $\vec{a}=\hat{i}+8\hat{j}+4\hat{k}$

$|\vec{a}|=\sqrt{1+64+16}=\sqrt{81}=9$ m/s${}^2$