Consider an object on which the net force is a resistive force proportional to the square of its speed. For example, assume that the resistive force acting on a speed skater is f = ─ kmv2, where k is a constant and m is the skater’s mass. The skater crosses the finish line of a straight-line race with speed v0 and then slows down by coasting on his skates. Show that the skater’s speed at any time t after crossing the finish line is v (t) = v0/(1 + ktv0). This problem also provides the background for the two following problems.