A variable force F acts along the x -axis given by F = 3 x 2 - 2 x + 1 N . The work done by the force when a particle of mass 100 g moves from x = 50 c m to x = 100 c m is

Question

A variable force F acts along the x -axis given by F = 3 x 2 - 2 x + 1 N . The work done by the force when a particle of mass 100 g moves from x = 50 c m to x = 100 c m is, 0.625 J, 6.25 J, 0.0625 J, 62.5 J

MARKS App · Accepted Answer

x i n i t i a l = 50 c m x f i n a l = 100 c m Therefore work done by the variable force, W = ∫ x i n i t i a l x f i n a l F . d x W = ∫ 0.5 1 3 x 2 - 2 x + 1 d x W = x 3 - x 2 + x 0.5 1 W = 1 - 0 . 5 3 - 1 - 0 . 5 2 + 1 - 0.5 W = 0.875 - 0.75 + 0.5 W = 0.625 J

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