Consider an object on which the net force is a resistive forceproportional to th

Question

Consider an object on which the net force is a resistive forceproportional to the square of its speed.For example,assume theresistive force acting on a speed skater is  
f=-kmv2,where k is a constant andm is the skater's mass.The skater crosses the finish lineof a straight-line race with speed v0 and thenslows down by coasting on his skates.Show that the skater's speedat any time t after crossing the finish line isv(t)=v0/(1+ktv0). Thank you very much! Consider an object on which the net force is a resistive forceproportional to the square of its speed.For example,assume theresistive force acting on a speed skater is  
f=-kmv2,where k is a constant andm is the skater's mass.The skater crosses the finish lineof a straight-line race with speed v0 and thenslows down by coasting on his skates.Show that the skater's speedat any time t after crossing the finish line isv(t)=v0/(1+ktv0). Thank you very much! Thank you very much!

Explanation / Answer

F = m a = m dv/dt = - k m v2 dv / v2 = - k dt 1 / v = k t + C   and at t = 0   C = 1 /v0 v = 1 / (k t + 1 / v0) = v0 /(v0 k t + 1) v = 1 / (k t + 1 / v0) = v0 /(v0 k t + 1)

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