A body of mass 2 kg begins to move under the action of a time dependent force given by F⃗=(6 t î+6 t² ĵ) N. The power developed by the force at the time t is given by:

Solution

Physics sir · 3 steps

Power is F dot v, so first build v from F by dividing by mass and integrating from rest.

1. Find acceleration. Divide the force by the mass: a⃗ = F⃗/m = (3t î + 3t² ĵ) m s⁻².
2. Find velocity. The body begins to move, so it starts from rest at t = 0. Integrating each component from 0 to t gives v⃗ = (3/2t² î + t³ ĵ) m s⁻¹.

   P = F⃗·v⃗ = (6t)(3/2t²) + (6t²)(t³)

3. So. P = 9t³ + 6t⁵, in watts. That is option (d).

The idea to keep. Instantaneous power is always F⃗·v⃗. When F depends on time, get v by integrating F⃗/m, use the starting velocity, then dot component by component.

Answer from the NTA final answer key. Solution by PrepWiser.