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}=( 2t\hat{i}+3t^{2}\hat{j} ]) N, $ , where $ \hat{i} and \hat{j} $ are unit vectors alogn x and y axis. What power will be developed by the force at the time t?
Options:
A) $ ( 2t^{2}+3t^{3} )W $
B) $ ( 2t^{2}+4t^{4} )W $
C) $ ( 2t^{3}+3t^{4} )W $
D) $ ( 2t^{3}+3t^{5} )W $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Given force $ \vec{F}=2t\hat{i}+3t^{2}\hat{j} $
According to Newton’s second law of motion, $ m\frac{d\vec{v}}{dt}=2t\hat{i}+3t^{2}\hat{j} $
$ (m=1kg) $
$ \Rightarrow \int\limits_0^{{\vec{v}}}{d\vec{v}} = \int\limits_0^{t}{( 2t\hat{i} + 3t^{2}\hat{j} )dt\Rightarrow \vec{v} = t^{2}\hat{i} +t^{3}\hat{j}} $
Power $ P = \vec{F}-\vec{v} ( 2t\hat{i}+ 3t^{2}\hat{j} ). ( t^{2}\hat{i} +t^{3}\hat{j} ) $
$ =( 2t^{3}+3t^{5} )W $
