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

Step-by-step solution

According to work energy theorem, aligned & W= K E . W= 1 2 m v₂^2- 1 2 m v₁^2 & F d x= K E f- 1 2 10 100 & F d x= K E f-500 & ₂₀³⁰-0.1 x d x= K E f-500 & -0.1 [ x^2 2 ]₂₀³⁰= K E f-500 & -0.1 [ 900-400 2 ]= K E f-500 aligned K _ E _ f =500-25=475 ~J