Serway & Jewett — Circular Motion and Other Applications of Newton's Laws: Problem 22

Assume the resistive force acting on a speed skater is proportional to the square of the skater’s speed \( v \) and is given by \( f = -kmv^2 \), 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 \( v(t) = v_i / (1 + ktv_i) \).