A body of mass 2 kg begins to move under the action of a time dependent force given by F → = 6 t i ^ + 6 t 2 j ^ N . The power developed by the force at the time t is given by:

Given: F → = 6 t i ^ + 6 t 2 j ^ N Now, F → = m a → = 6 t i ^ + 6 t 2 j ^ ⇒ a → = F → m = 3 t i ^ + 3 t 2 j ^ Hence, velocity v → = ∫ 0 t a → d t = 3 t 2 2 i ^ + t 3 j ^ Required power, P = F → . v → = 9 t 3 + 6 t 5 W

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PhysicsW.E.P.PowerEasy2 minQB

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A body of mass $2 kg$ begins to move under the action of a time dependent force given by $\vec{F} = (6 t \hat{i} + 6 t^{2} \hat{j}) N$ . The power developed by the force at the time $t$ is given by:

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Solution:

Given: $\vec{F} = (6 t \hat{i} + 6 t^{2} \hat{j}) N$

Now, $\vec{F} = m \vec{a} = (6 t \hat{i} + 6 t^{2} \hat{j})$

$\Rightarrow \vec{a} = \frac{\vec{F}}{m} = (3 t \hat{i} + 3 t^{2} \hat{j})$

Hence, velocity $\vec{v} = \int_{0}^{t} \vec{a} d t = \frac{3 t^{2}}{2} \hat{i} + t^{3} \hat{j}$

Required power, $P = \vec{F} . \vec{v} = (9 t^{3} + 6 t^{5}) W$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Power

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