### NEET Solved Paper 2016 Question 39

##### 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 along 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:

$ \vec{F}=2t\hat{i}+3t^{2}\hat{j}\ $ $ 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 $ =\vec{F}.\vec{v}=(2t^{3}+3t^{5})W $