1. The problem statement, all variables and given/known data A truck hauling a big tank of oil starts at position x=D (Chicago) and heads due west (–x direction) toward its destination at x = 0 (Des Moines). At Chicago, the total mass of the loaded truck is M and the mass of oil it is carrying is λM. (Thus M(1–λ) is the "tare" mass = the mass of the truck when it is empty.) The driver starts from rest at time t = 0 with his engines set to deliver a constant force of magnitude F throughout the trip. Unfortunately, the trucker's oil tank is leaking: it is losing oil at a constant rate-per-unit-distance of dm/dx=λM/D Ignore the small change in m from the truck's consumption of gasoline (it's tiny compared to the truck's mass). (a) Calculate m(x) in terms of x and the given constants D, M, λ, and/or F. (b) Calculate the truck's kinetic energy as a function of x and the given constants. (c) At what position x does the truck reach it's maximum speed and at what position does it reach it's maximum kinetic energy? 2. Relevant equations dm/dx=λM/D F=dp/dt T=.5mv² 3. The attempt at a solution I think I've got part a right as λ, M, and D are constants so: m(x)=λMx/D+(1-λ)M and I checked it where x=D the mass is M, so I think that is the right answer. As for parts b and c , I honestly have no idea where to begin solving for velocity. I understand to find T that I'll have to use my m(x) but I don't know what force equation to set up to solve for velocity.