JEE Main: Find Power Using F · v Concept 💡
❓ Question An object of mass 1000 g experiences a time dependent force F ⃗ = ( 2 t i ^ + 3 t 2 j ^ ) N \vec F = (2t \,\hat i + 3t^2 \,\hat j)\, \text{N} The power generated by the force at time t is: 🖼 Question Image ✍️ Short Solution This is a Power = F · v question. 👉 Time dependent force 👉 Velocity changes with time 👉 First find velocity using Newton’s 2nd Law Then apply: P = F ⃗ ⋅ v ⃗ P = \vec F \cdot \vec v 🔷 Step 1 — Convert Mass & Use Newton’s Law (MOST IMPORTANT 💯) Given mass: 1000 g = 1 kg 1000 \text{ g} = 1 \text{ kg} Using: F ⃗ = m a ⃗ \vec F = m\vec a So acceleration: a ⃗ = F ⃗ \vec a = \vec F a ⃗ = ( 2 t i ^ + 3 t 2 j ^ ) \vec a = (2t \hat i + 3t^2 \hat j) 🔷 Step 2 — Find Velocity by Integration Since: a ⃗ = d v ⃗ d t \vec a = \frac{d\vec v}{dt} Integrate: x-component: v x = ∫ 2 t d t = t 2 v_x = \int 2t\, dt = t^2 y-component: v y = ∫ 3 t 2 d t = t 3 v_y = \int 3t^2\, dt = t^3 So velocity: v ⃗ = ( t 2 i ^...