Q 11-05-208JEE MainJEE Main 2025 (7 Apr, Shift 1)Medium
An object of mass $1000\ \text{g}$, starting from rest at $t = 0$, experiences a time dependent force $\vec F = (2t\,\hat i + 3t^2\,\hat j)\ \text{N}$. The power generated by the force at time $t$ is:
Answer: (D) $(2t^3 + 3t^5)\ \text{W}$
With $m = 1\ \text{kg}$, $\vec a = 2t\,\hat i + 3t^2\,\hat j$. Integrating from rest:
$$\vec v = t^2\,\hat i + t^3\,\hat j$$
$$P = \vec F\cdot\vec v = (2t)(t^2) + (3t^2)(t^3) = (2t^3 + 3t^5)\ \text{W}$$
Solution by Sreeraj P, M.Sc Physics