InterviewSolution
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InterviewSolution
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A body of mass `1 kg` begins to move under the action of a time dependent force `vec F = (2 t hat I + 3 t^(2) hat j) N`, where `hat i` and `hat j` are unit vectors along x-and y-axes. What power will be developed by the force at the time `t` ?A. `(2t^(2)+4t^(4))W`B. `(2t^(3)+3t^(4))W`C. `(2t^(3)+3t^(5))W`D. `(2t+3t^(3))W` |
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Answer» Correct Answer - c `(c )` According to question, a body of mass 1 kg begins to move under the action of time dependent force, `F=(2thati+3t^(2)hatj)N` Where` hati "and" hatj` are unit vectors along X and Y-axes. `thereforeF=ma` `implies a=F/m` `impliesa=((2thati+3^(2)thatj))/(1)" "(therefore m=1kg)` `impliesa=(2thati+3^(2)thatj)m//s^(2)` `therefore` accelaration, `a=(dv)/(dt)` `implies" "dv= a dt` Integrating both sides, we get `intdv=inta" "dt=int(2thati+3t hatj)dt` `v=t^(2)hati+t^(3)hatj` `therefore` Power developed by the force at the time t will be given as `P=F.v=(2thati+3thatj).(t^(2)hati+t^(3)hatj)` `=(2t.t^(2)+3t^(2).t^(3))` `P=(2t^(3)+3t^(5))W` |
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