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A body of mass \( 1 \mathrm{~kg} \) begins to move under the action of a time dependent force \( \mathbf{F}=\left(2 t \hat{\mathbf{i}}+3 t^{2} \hat{\mathbf{j}}\right) \mathrm{N} \), where \( \hat{\mathbf{i}} \) and \( \hat{\mathbf{j}} \) are unit vectors along \( X \) and \( Y \)-axes.
What power will be developed by the force at the time \( t \) ?
(a) \( \left(2 t^{2}+4 t^{4}\right) \mathrm{W} \)
(b) \( \left(2 t^{3}+3 t^{4}\right) \mathrm{W} \)
(c) \( \left(2 t^{3}+3 t^{5}\right) \mathrm{W} \)
(d) \( \left(2 t+3 t^{3}\right) \mathrm{W} \)
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