A body of mass 2 kg begins to move under the action of a time dependent force given by The power developed by the force at the time is given by

Question

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 [2024]

Smart Achievers · Accepted Answer

(4)

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

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

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

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

$P = \vec{F} \cdot \vec{v} = (9 t^{3} + 6 t^{5}) W$

Solution

Q.
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 [2024]

1 $(6 t^{4} + 9 t^{5}) W$

2 $(3 t^{5} + 6 t^{5}) W$

3 $(9 t^{5} + 6 t^{3}) W$

4 $(9 t^{3} + 6 t^{5}) W$

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Solution

Q. A body of mass 2 kg begins to move under the action of a time dependent force given by F→=(6ti^+6t2j^)N. The power developed by the force at the time t is given by [2024]

1 (6t4+9t5)W

2 (3t5+6t5)W

3 (9t5+6t3)W

4 (9t3+6t5)W