A force F = α + β x 2 acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant α = 1 N then β will be

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F = α + β x 2 Work done ∫ d w = ∫ F ⋅ d x ​ ⇒ Δ W = ∫ F ⋅ d x = ∫ ( α + β x 2 ) d x ⇒ Δ W = ​ αx + 3 β x 3 ​ ​ 0 1 ​ = α + 3 β ​ = 5 ​ Given α = 1 So, 3 β ​ = 4 ⇒ β = 12 N / m 2

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