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A body of mass 1 kg begins to move under the action of a time dependent force \text{\vec F} = \left( {2\text{t}\hat i + 3\text{t}^2 \hat j} \right)\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?

Answers (1)

 we know that

f=\frac{\vec{dp}}{dt}=m\frac{d\vec{v}}{dt}

2+{\hat{i}}+3t^{2}\hat{j}=m\frac{d\vec{v}}{dt}

=>\int_{0}^{\vec{v}}\vec{d}v=\int_{0}^{t}\left ( 2t\hat{i}+3t^{2}\hat{j} \right )dt

\therefore \vec{v}=t^{2}\hat{i}+t^{3}\hat{j}

\vec{P}=\vec{F}. \vec{V}

=\left ( 2t\hat{i}+3t^{2}\hat{j} \right ).\left ( t^{2}\hat{i}+t^{3}\hat{j} \right )

=\left ( 2t^{3}+3t^{5} \right )w

 

 

 

 

 

 

 

 

Posted by

Safeer PP

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