A block of mass m is at rest at the origin at t = 0. It is pushed with constant force F₀ from x = 0 to x = L across a horizontal surface whose coefficient of kinetic friction is m_k = m₀ (1 – x/L).

That is, the coefficient of friction decreases from m 0 at x = 0 to zero at x = L.

a. Use what you’ve learned in calculus to prove that

b. Find an expression for the block’s speed as it reaches position L?