What is the Equation for Resistive Force and Speed in a Straight-Line Race?

[gaborfk]

Consider an object 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=-k*m*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(i) and the slows down by coasting on his skates. Show that his speed at time "t", any time after the finish line is equal to Vf=Vi/(1+Vi*k*t).

I know that the masses cancel out and I get this m dv/dt= kmV^2 since "mass times acceleration equals force".

But now what? How does the Vi gets introduced?

Thank you in advance!

 

[arildno]

Don't double post!

 

[gaborfk]

Sorry, I posted the first one in the wrong forum.