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  4. A force of (5 + 3x) N acting on a body of mass 20 kg along the x - axis displaces it from x = 2 m to x = 6 m . The work done by the force is

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Q. A force of $ (5 + 3x)\,N $ acting on a body of mass $ 20 \,kg $ along the $ x $ - axis displaces it from $ x = 2\,m $ to $ x = 6\, m $ . The work done by the force is

UPSEEUPSEE 2009Work, Energy and Power

Solution:

Force $F=(5+3 x) N$
Work done $W=\int\limits_{x_{1}}^{x_{2}} F \cdot d x=\int\limits_{2}^{6}(5+3 x) d x$
$=\left[5 x+\frac{3 x^{2}}{2}\right]_{2}^{6}=68 \,J$