An object of mass 1000 g experiences a time dependent force F⃗=(2 t î+3 t² ĵ) N. The power generated by the force at time t is:

Solution

Physics sir · 3 steps

Power needs velocity, so first integrate the acceleration to get velocity, then take F⃗ · v⃗.

1. Find acceleration. The mass is 1000 g = 1 kg, so a⃗ = F⃗/m = (2t î + 3t² ĵ) m s⁻².
2. Integrate for velocity. The acceleration changes with time, so you cannot use v = at. Integrate from t = 0, taking the object to start from rest: v⃗ = ∫₀ᵗ a⃗ dt = t² î + t³ ĵ.

   P = F⃗ · v⃗ = (2t)(t²) + (3t²)(t³)

3. So. P = (2t³ + 3t⁵) W, which is option (c).

The idea to keep. Power is always F⃗ · v⃗. When the force depends on time, get v⃗ by integrating a⃗, never by writing v = at.

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