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A force F act...

Question

A force F acting on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object from x = 0 to x = 6 m is

18.0 J

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13.5 J

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4.5 J

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9.0 J

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Solution

The correct option is A 13.5 J
W = $\int$ F.dx = Area under the curve
$(3 \times 3) + \frac{1}{2} \times (3) (3) = 13.5 J$

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F

x

N

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m

x = 0

x = 6 m

F

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N

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m

x = 0 to x = 6 m

x = 2 m

x = 4 m

x

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F (x) = \sqrt{6 x - x^{2}}

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