A block of mass 10kg is moving in x-direction with constant speed of 10m/s. It is subjected to a retarding force F=0.1x joule/metre during its travel from x=20m to x=30m. Its final K.E will be:

Given : Retarding force F=0.1x for 20<x<30
Mass of the block m=10kg
∴F=m(-a) (- sign shows retardation)
ma = -0.1x
(10)a = -0.1x
a = -0.01x
We know that a = v(dv/dx)
v(dv/dx) = -0.01x
∫₁₀ᵛ vdv = -0.01 ∫₂₀³⁰ xdx
v²/2 |₁₀ᵛ = -0.01 × x²/2 |₂₀³⁰
v² - 10² = -0.01 × (30² - 20²)
v² = 100 - 0.01 × (900 - 400)
v² = 100 - 5
v² = 95
Final kinetic energy E = (1/2)mv² = (1/2) × 10 × 95 = 475J