An object of mass 1000 g experiences a time dependent force F = ( 2 t i ^ + 3 t 2 j ^ ) N . The power generated by the force at time t is :

F = ( 2 t i ^ + 3 t j ^ ) N m = 1000 gm = 1 kg F = m a , a = 2 t i ^ + 3 t 2 j ^ dt d v = 2 t i ^ + 3 t 2 j ^ v = t 2 i ^ + t 3 j ^ Power, P = F ⋅ v P = ( 2 t i ^ + 3 t 2 j ^ ) ⋅ ( t 2 i ^ + t 3 j ^ ) P = ( 2 t 3 + 3 t 5 ) W

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PhysicsW.E.P.PowerMedium2 minQB

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An object of mass 1000 g experiences a time dependent force $F = (2 t \hat{i} + 3 t^{2} \hat{j}) N$ . The power generated by the force at time $t$ is :

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Answer:

Solution:

$F = (2 t \hat{i} + 3 t \hat{j}) N m = 1000 gm = 1 kg F = m a, a = 2 t \hat{i} + 3 t^{2} \hat{j} \frac{d v}{dt} = 2 t \hat{i} + 3 t^{2} \hat{j}$
$v = t^{2} \hat{i} + t^{3} \hat{j}$
Power, $P = F \cdot v$
$P = (2 t \hat{i} + 3 t^{2} \hat{j}) \cdot (t^{2} \hat{i} + t^{3} \hat{j}) P = (2 t^{3} + 3 t^{5}) W$

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

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