A body of mass 1 kg begins to move under the action of time dependent force ⃗F=(2tı̂+3t²ȷ̂) N, where ı̂ and ȷ̂ are unit vectors along x and y axis. What power will be developed by the force at the time t?

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(2) (2t³+3t⁵) W. Given: m=1 kg starting from rest, ⃗F=2tı̂+3t²ȷ̂ N. Idea: the force varies, so the velocity has to be built up by integrating the acceleration before the power can be found. ⃗a=(⃗F)/m=2tı̂+3t²ȷ̂. ⃗v=∫⃗a dt=t²ı̂+t³ȷ̂ (starting from rest, so no constant). P=⃗F·⃗v=(2t)(t²)+(3t²)(t³). P=(2t³+3t⁵) W.

A body of mass 1 kg begins to move under the action of time dependent force ⃗F=(2tı̂+3t²ȷ̂) N, where ı̂ and ȷ̂ are unit vectors along x and y axis. What power will be developed by the force at the time t?

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