Finding coefficient of kinetic friction?

Question

A hockey puck on a frozen pond with an initial speed of 21.9 m/s stops after sliding a distance of 242.1 m. Calculate the average value of the coefficient of kinetic friction between the puck and the ice.

Answer 1

Let's consider a few equations
1. F=f
F=ma
f=umg (force due to friction or apposing motion)
m - mass of the puck
a - acceleration of the puck (negative)
g = 9.81 m/s^2
u - coefficient of friction
we have then
a=ug
so u=a/g (we will return to it later)

also we know that
S= .5at^2
t- time of travel under acceleration a
S- distance covered

Also velocity V
V=at
t=V/a
Since S= .5at^2
S=.5(a)(V/a)^2
S=(.5V^2)/a then
a=(V^2)/2S

Finlay since u=a/g
we have
u=(V^2)/2Sg
u= (21.9 ^2)/(2 x 242.1 9.81)=0.101