Problem 1 (20 points) The figure below shows a scheme for one of the simplest mechanical systems: a cart having mass M, moving on wheels on a surface with dynamic friction coefficient b. The cart could represent a vehicle or a dolly used to move loads in a factory. We want do describe the dynamics of its speed. Suppose the cart has an engine, which produces a force u in the direction shown in the figure. M u Friction ~ bv 1. Using Newton's law, write the ODEs describing the velocity of the cart. 2. Find the exact solution of the ODEs assuming initial velocity v(0) = v and u = = 1. 3. What is the velocity of the system for t , i.e. the steady state velocity?