Chapter 6, Problem 33P

Assume the resistive force acting on a speed skater is proportional to the square of the skater’s speed v and is given by 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 v_i 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) = v_i/(1 + ktv_i).