Q 11-05-088JEE MainJEE Main 2024 (31 Jan, Shift 2)Medium
A body of mass $2\ \text{kg}$ begins to move under the action of a time dependent force given by $\vec F = (6t\,\hat i + 6t^2\,\hat j)\ \text{N}$. The power developed by the force at time $t$ is given by:
Answer: (D) $(9t^3 + 6t^5)\ \text{W}$
$\vec a = \dfrac{\vec F}{m} = 3t\,\hat i + 3t^2\,\hat j$. Starting from rest,
$$\vec v = \int_0^t\vec a\,dt = \tfrac32t^2\,\hat i + t^3\,\hat j$$
$$P = \vec F\cdot\vec v = 6t\cdot\tfrac32t^2 + 6t^2\cdot t^3 = 9t^3 + 6t^5\ \text{W}$$
Solution by Sreeraj P, M.Sc Physics