A body of mass 1 kg begins to move under the action of a time dependent force \(\vec{F}\) = (2t î + 3t² ĵ) N, where î and ĵ are unit vectors along x and y axis. What power will be developed by the force at the time t?

(2t³ + 3t⁵ )W

\(\vec{F} = m \vec{a}\)

m = 1 kg

⇒ \(\vec{a} = [2t î + 3t^2 ĵ] m/s^2 = \frac{d\vec{v}}{dt} \)

\(\vec{v} = t^2 \hat{i}+ t^3 \hat{j} \) 

\(\vec{F} = \) (2t î + 3t² ĵ) N

P = \(\vec{v}.\vec{F}\) 

   = \(2t^3 \hat{i}+ 3t^5 \hat{j} \)