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Physics · PYQ NEET UG 2016(1)
हिन्दीA body of mass \( 1\text{ kg} \) begins to move under the action of a time dependent force \( \vec{F} = (2t\,\hat{i} + 3t^2\,\hat{j})\text{ N} \), 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 \( t \)?
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Correct answer · Option A
\( (2t^3 + 3t^5)\text{ W} \)
Explanation
Acceleration \( \vec{a} = \frac{\vec{F}}{m} = 2t\,\hat{i} + 3t^2\,\hat{j} \). Velocity \( \vec{v} = \int \vec{a}\,dt = t^2\,\hat{i} + t^3\,\hat{j} \). Power \( P = \vec{F} \cdot \vec{v} = (2t)(t^2) + (3t^2)(t^3) = 2t^3 + 3t^5 \).
