Q 11-05-054JEE MainJEE Main 2026 (4 Apr, Shift 1)Medium
A body of mass $2$ kg begins to move under the influence of time dependent force $\vec{F} = (2t\hat{i} + 6t^2\hat{j})$ N, where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$-axis respectively. The power produced by the force at $t = 2$ s is ______ W.
Numerical value type. Enter your answer.
Answer: 200
$\vec{a} = t\hat{i} + 3t^2\hat{j}$, so starting from rest $\vec{v} = \dfrac{t^2}{2}\hat{i} + t^3\hat{j}$.
At $t = 2$ s: $\vec{v} = 2\hat{i} + 8\hat{j}$ m/s and $\vec{F} = 4\hat{i} + 24\hat{j}$ N.
$P = \vec{F} \cdot \vec{v} = 8 + 192 = 200$ W.
Solution by Sreeraj P, M.Sc Physics