Ablock of mass m is at rest at the origin at t = 0. it is pushed with constant force fo from x= 0 to x=l across a horizontal surface whose coefficient of kinetic friction is μk = μo (1-x/l) that is, the coefficient of friction decreases from μo at x=0 to zero at x= l. we would like to know the velocity of the block when it reaches some position x. finding this requires an integration. however, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. to get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dvxdx.