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  4. A particle of mass 500 gm is moving in a straight line with velocity v=b x5 / 2. The work done by the net force during its displacement from x=0 to x =4 m is: (. Take . b =0.25 m -3 / 2 s -1).

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Q. A particle of mass $500\, gm$ is moving in a straight line with velocity $v=b x^{5 / 2}$. The work done by the net force during its displacement from $x=0$ to $x =4 \,m$ is : $\left(\right.$ Take $\left. b =0.25 \,m ^{-3 / 2} s ^{-1}\right)$.

JEE MainJEE Main 2022Work, Energy and Power

Solution:

By work energy theorem
work done by net force $=\Delta K$.E.
$\Rightarrow W =\frac{1}{2} mu _{ f }^{2}-\frac{1}{2} mu _{ i }^{2} $
$ w =\frac{1}{2} \times 0.5 \times(0.25)^{2} \times(4)^{5} $
$ w =16\, J $