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A block is initially at rest on a smooth horizontal surface, now a variable force $F = (5 x - x^{2}) \overset{\land}{i}$ N acts on the block. The value of potential energy of a block between points x=0 and x=10m, (where kinetic energy of block is 10J and block has total energy equal to its maximum potential energy)

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12.8J

14.8J

10.8J

11.8J

answer is A.

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Detailed Solution

$E = \int_{0}^{x} (5 x - x^{2}) d x = \frac{5 x^{2}}{2} - \frac{x^{3}}{3}$

$\frac{d E}{d x} = 0 f o r E_{\max} \frac{5 (2 x)}{2} - {\frac{3 x}{2}}^{2} = 0 x = 5$

$E_{\max} = \frac{5}{2} \times {(5)}^{2} - \frac{1}{3} {(5)}^{3} = 20.8 J$

At a point , $K = 10.0 J, P E = 10.8 J$

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