A block of mass 10 kg is moving in x -direction with a constant speed of 10 m / sec . It is subjected to a retarding force F = − 0.1 x joule/m eter during its travel from x = 20 meter to x = 30 meter.

Question

A block of mass 10 kg is moving in x -direction with a constant speed of 10 m / sec . It is subjected to a retarding force F = − 0.1 x joule/m eter during its travel from x = 20 meter to x = 30 meter. Its final kinetic energy will be

TestHub · Accepted Answer

According to work energy theorem, ⇒ ⇒ ⇒ ⇒ ⇒ ​ W = Δ K ⋅ E . ⇒ W = 2 1 ​ m v 2 2 ​ − 2 1 ​ m v 1 2 ​ F ⋅ d x = K ⋅ E ⋅ f − 2 1 ​ × 10 × 100 F ⋅ d x = K ⋅ E ⋅ f − 500 ∫ 20 30 ​ − 0.1 x d x = K ⋅ E ⋅ f − 500 − 0.1 [ 2 x 2 ​ ] 20 30 ​ = K ⋅ E ⋅ f − 500 − 0.1 [ 2 900 − 400 ​ ] = K ⋅ E ⋅ f − 500 ​ ⇒ K ⋅ ​ E ⋅ f ​ = 500 − 25 = 475 J

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