A body of mass 1 kg moves along a straight line with a velocity $v = 2x^{2}$. The work done by the b

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A body of mass 1 kg moves along a straight line with a velocity $v = 2x^{2}$. The work done by the body during displacement from $x = 0$ to 5 m is $\_\_\_\_$ J.

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Sol. [Key Concept: Work done $= \Delta\ KE = \frac{1}{2}\ m(v_{f}^{2} - v_{i}^{2})$ with $v = 2x^{2}$ evaluated at $x = 0$ and $x = 5$.]$$w.\Delta = \Delta K.E$$$$\begin{matrix} & \ = \frac{1}{2}	ext{ }m\left( v_{f}^{2} - v_{i}^{2} ight) \ & \ = \frac{1}{2} 	imes 1\left\lbrack \left( 2(5)^{2} ight)^{2} - (2(0))^{2} ightbrack^{0} \ & \ = \frac{1}{2} 	imes 50 	imes 50 = 1250	ext{ }J \end{matrix}$$

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