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