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

AI Thread Summary
The discussion focuses on deriving the equation for an object's speed after experiencing a resistive force proportional to the square of its speed, specifically for a speed skater. The resistive force is expressed as F = -k*m*V^2, leading to the differential equation m dv/dt = -k*m*V^2. The solution reveals that the skater's speed at time "t" after crossing the finish line is given by Vf = Vi/(1 + Vi*k*t). The mass cancels out in the equation, simplifying the analysis. The introduction of initial speed Vi is crucial for determining the skater's speed over time.
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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!
 
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