A body of mass 1 kg begins to move under the action of a time dependent force F=(2ti+3t^2j)N, where i and j are unit vectors along X and Y axes. What power will be developed by the force at the time…

Question

A body of mass 1 kg begins to move under the action of a time dependent force F=(2ti+3t^2j)N, where i and j are unit vectors along X and Y axes. What power will be developed by the force at the time (t )? [NEET 2016]

Accepted Answer

Correct answer: C. (c) Given, m=1 g F=(2ti+3t^2j)N ∵ F= ma ⇒a= Fm ⇒a= (2ti+3t^2j)1 ( ∵m=1 kg ) ⇒a=(2ti+3t^2j)m/s^2 ∵ acceleration, a= dv dt ⇒ dv=a dt Integrating both sides, we get dv= a dt= (2ti+3t^2j) dtv=t^2i+t^3j ∵ Power developed by the force at the time t will be given as P=F v=(2ti+3t^2j) (t^2i+t^3j)=(2t t^2+3t^2 t^3)P=(2t^3+3t^5)W

$A body of mass 1 kg begins to move under the action of a time dependent force F = (2 t i + 3 t^{2} j) N, where i and j are unit vectors along X and Y axes. What power will be developed by the force at the time (t) ? [NEET 2016]$

Solution

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