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NEET NEET SOLVED PAPER 2016 Phase-I

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

    A)  \[(2{{t}^{2}}+3{{t}^{3}})W\]      

    B)  \[(2{{t}^{2}}+4{{t}^{4}})W\]

    C)  \[(2{{t}^{3}}+3{{t}^{4}})W\]      

    D)   \[(2{{t}^{3}}+3{{t}^{5}})W\]

    Correct Answer: D

    Solution :

                     \[\vec{F}=2t\hat{i}+3{{t}^{2}}\hat{j}\,\]                 \[m\frac{d\vec{v}}{dt}\,=2t\hat{i}+3{{t}^{2}}\hat{j}\]     \[\,(m=\,1kg)\]                 \[\Rightarrow \]                \[\int\limits_{0}^{{\vec{v}}}{d\vec{v}}=\int\limits_{0}^{t}{(2t\hat{i}+3{{t}^{2}}\hat{j})}dt\Rightarrow \vec{v}={{t}^{2}}\hat{i}+{{t}^{3}}\hat{j}\]                 Power \[=\vec{F}.\vec{v}=(2{{t}^{3}}+3{{t}^{5}})W\]


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