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

Question

After crossing the finish line, a speed skater stops pushing and continues to glide. the resistive force acting on the skater is f=-kmv2

you know the following
k= a constant
m= mass of skater
v= speed of skater anytime after she crosses the finish line
v0= speed of the skater as she crosses the finish line.

g= accel. due to gravity

parts one and two are write and then solve newton's second law eqn. for her speed after the finish line

part 3 is describe the time ( in terms of m and k ) that it takes for the skater to reduce his or her speed by a factor of two - after crossing the finish line.

Explanation / Answer

As the skater applied no force after crossed the finsh line, the acceleration of the scater after crossing the finish line will be due to only the resistive force Therefore ma = -kmv2 a = -kv2 naegative sign indicates the deceleartion The equation of motion of the scater after crossing the finishline, when the velocity is 0.5v0 is 0.5v0 = v0 + at -0.5v0 = -k(0.5v0)2t t = 2/kv0 naegative sign indicates the deceleartion The equation of motion of the scater after crossing the finishline, when the velocity is 0.5v0 is 0.5v0 = v0 + at -0.5v0 = -k(0.5v0)2t t = 2/kv0

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