A position dependent force, F = (7 - 2x + 3x²) N acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5 m. The work done in joule is (a) 135 (b) 270 (c) 35 (d) 70

Answer: (a). W = ∫₀⁵ (7 - 2x + 3x²) dx = [7x - x² + x³]₀⁵ W = 35 - 25 + 125 = 135 J (mass is not needed) So the answer is (a) 135.

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Work by a Variable Force

A position dependent force, $F = (7 - 2x + 3x^2)\text{ N}$ acts on a small body of mass $2\text{ kg}$ and displaces it from $x = 0$ to $x = 5\text{ m}$ . The work done in joule is

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Answer: (a)

$W = \int_0^5 (7 - 2x + 3x^2)\,dx = \left[7x - x^2 + x^3\right]_0^5$
$W = 35 - 25 + 125 = 135$ J (mass is not needed)
So the answer is (a) 135.

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