Suppose that a particle of mass m is in a fluid medium and is given an initial velocity vo to the right from the origin. in class we showed that fluid drag is proportional to velocity at very low speeds but proportional to v at higher speeds. to capture this shift, the best force law to use is f( -cv, where b and c are properties of the fluid. (note that v > 0 always, so f < 0 always.) (a) state the general way to solve for vx) directly (without having to solve for the time- evolution) when the force varies only with velocity, f-f(v). find the distance the particle travels before coming to rest. problem with fbv, and by taking the limit c-0 in your solution for part (b). (for the (b) find v(x) for this system, and use it to sketch a complete phase portrait for this system. (c) show that v(x) becomes a straight line if c-0. do this in two ways. by redoing the