Q 11-05-097JEE MainJEE Main 2023 (24 Jan, Shift 2)Medium
A body of mass $1\ \text{kg}$ begins to move under the action of a time dependent force $\vec F=\left(t\hat i+3t^2\hat j\right)$ N, where $\hat i$ and $\hat j$ are the unit vectors along $x$ and $y$ axis. The power developed by above force, at the time $t=2$ s, will be ______ W.
Numerical value type. Enter your answer.
Answer: 100
With $m=1\ \text{kg}$, $\vec a=\vec F$, so starting from rest $\vec v=\dfrac{t^2}{2}\hat i+t^3\hat j$.
At $t=2$: $\vec F=2\hat i+12\hat j$, $\vec v=2\hat i+8\hat j$.
$P=\vec F\cdot\vec v=4+96=100\ \text{W}$.
Solution by Sreeraj P, M.Sc Physics