A body of mass 1 kg begins to move under the action of a

A body of mass 1 kg begins to move under the action of a time dependent force F^{^→} = (2tî + 3t²ĵ) N, where î and ĵ are unit vectors alogn x and y axis. What power will be developed by the force at the time t?

Given force F^{^→} = 2tî + 3t²ĵ
According to Newton's second law of motion,

m	dv^{^→}	= 2tî + 3t²ĵ (m = 1 kg)
	dt

⇒ v^{^→} = t²î + t³ĵ
Power P = F^{^→} . v^{^→} = (2tî + 3t²ĵ) . (t²î + t³ĵ)
= (2t³ + 3t⁵)W