SATHEE: Work Energy And Power Question 273

Work Energy And Power Question 273

Question: A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}]) N,$ , where $\hat{i} a n d \hat{j}$ are unit vectors alogn x and y axis. What power will be developed by the force at the time t?

Options:

A) $(2 t^{2} + 3 t^{3}) W$

B) $(2 t^{2} + 4 t^{4}) W$

C) $(2 t^{3} + 3 t^{4}) W$

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

Show Answer

Answer:

Correct Answer: D

Solution:

[d] Given force $\vec{F} = 2 t \hat{i} + 3 t^{2} \hat{j}$

According to Newton’s second law of motion, $m \frac{d \vec{v}}{d t} = 2 t \hat{i} + 3 t^{2} \hat{j}$

$(m = 1 k g)$

$\Rightarrow \int_{0}^{\vec{v}} d \vec{v} = \int_{0}^{t} (2 t \hat{i} + 3 t^{2} \hat{j}) d t \Rightarrow \vec{v} = t^{2} \hat{i} + t^{3} \hat{j}$

Power $P = \vec{F} - \vec{v} (2 t \hat{i} + 3 t^{2} \hat{j}) . (t^{2} \hat{i} + t^{3} \hat{j})$

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

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Work Energy And Power Question 273

Question: A body of mass 1 kg begins to move under the action of a time dependent force F→=(2ti^+3t2j^])N, , where i^andj^ are unit vectors alogn x and y axis. What power will be developed by the force at the time t?

Options:

Answer:

Solution:

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Question: A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}]) N,$ , where $\hat{i} a n d \hat{j}$ are unit vectors alogn x and y axis. What power will be developed by the force at the time t?