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
Concept. Power $P=\vec F\cdot\vec v$. With a time-dependent force from rest, get $\vec v$ by integrating $\vec a=\vec F/m$.
Step 1. Velocity. $\vec a=t\,\hat i+3t^2\,\hat j$; $\vec v=\dfrac{t^2}{2}\hat i+t^3\hat j$. At $t=2$: $\vec v=2\hat i+8\hat j$.
Step 2. Force at $t=2$. $\vec F=4\hat i+24\hat j$.
Step 3. Power. $P=4(2)+24(8)=8+192=200$ W.
Answer. $200$.
Solution by Sreeraj P, M.Sc Physics
