After crossing the finish line a speed skater stops pushing and continues to gli

Question

After crossing the finish line a speed skater stops pushing and continues to glide. the resitive force is fr=-bmv^2
b=constant
m=mass of skater
v=speed any time after crossing the finish line
v0=speed as skater crosses the finish line

g= acceleration due to gravity

hint: integral xndx=(xn+1)/(n+1)

1. write newtons second law for the skater any time after he crosses the finish line

2. Solve newtons second law equation to determine an expression for the speed of the skater any time after he crosses the finish line

3.Determine the time in terms of m and k that it takes the skater to reduce his speed by a factor of 2 after crossing the finish line

Explanation / Answer

a)Netwons second law is simply F = M*a where M is mass and a is acceleration of the object. For any time the the force on the skater is mdv/(t)dt = -bmv(t)^2 ; v(t) is velocity of skater at any time t which is the newtons second law b) solving the above equation involves integrating the equation such that we get an expression for the velocity of the skater. so the equation is dv(t)/dt = -bv(t)^2 integral v^-2*dv(t) = integral -b *dt -v(t)|(limit from v_0 to v(t)) = -b*t v(t) - v_0 = -b*t v(t) = v_0 -b*t c) final velocity = v_0/2 = v(t) so, v_0/2 = v_0 -b*t t = v_0/(2*b) I dont know where suddenly k comes from in the question. The answer to the third part will not depend on the mass.

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