Question

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 forve acting on a speed skater is f=-km[v^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-sub 0] 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-sub 0]/(1+k[v-sub 0]).

Assuming only the drag that is proportional to mV^2,
m dV/dt = - k m V^2
dV/V^2 = -k dt
Integrate both sides from t=0 to t
kt = 1/V(t) - 1/Vsubo
1/V(t) = 1/Vsubo + kt
V(t) = 1/[1/Vsubo + kt]
= Vsubo / [1 + (kVsubo*t)]
You left out a "t" term in your answer.

Answer 1

The question appears in the book Introductory Physics for Scientists and Engineers. The evaluation can be found at youtube url : watch?v=N3Y_MJREps0 .