A) \[\left( 2{{t}^{2}}+3{{t}^{3}} \right)W\]
B) \[\left( 2{{t}^{2}}+4{{t}^{4}} \right)W\]
C) \[\left( 2{{t}^{3}}+3{{t}^{4}} \right)W\]
D) \[\left( 2{{t}^{3}}+3{{t}^{5}} \right)W\]
Correct Answer: D
Solution :
[d] Given force \[\vec{F}=2t\hat{i}+3{{t}^{2}}\hat{j}\] According to Newton's second law of motion, \[m\frac{d\vec{v}}{dt}=2t\hat{i}+3{{t}^{2}}\hat{j}\] \[(m=1kg)\] \[\Rightarrow \int\limits_{0}^{{\vec{v}}}{d\vec{v}} = \int\limits_{0}^{t}{\left( 2t\hat{i} + 3{{t}^{2}}\hat{j} \right)dt\Rightarrow \vec{v} = {{t}^{2}}\hat{i} +{{t}^{3}}\hat{j}}\] Power \[\operatorname{P} = \vec{F}-\vec{v} \left( 2t\hat{i}+ 3{{t}^{2}}\hat{j} \right). \left( {{t}^{2}}\hat{i} +{{t}^{3}}\hat{j} \right)\] \[=\left( 2{{t}^{3}}+3{{t}^{5}} \right)W\]
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