If the coefficient of kinetic friction between the puck and the ice is 0.05, how far does the puck slide before coming to rest? solve this problem using conservation of energy.

According to newton's 3rd law of motion,

For every action, there is equal and opposite reaction. So if we move a body against a rough surface, there were be reaction against the force applied.

So using conservation of energy, we know:

Work done to move a body = Work done against Friction

So, Force applied * distance moved = coefficient of Friction * Normal Reaction * distance moved

For a body moving against a normal surface, Normal Reaction (R) = mg

or, mass * acceleration * distance (s) = ∪ * R * distance (s)

or, mass * (v^2/2s) = ∪ * mass * gravity

Now, s = stopping distance = v² / 2∪g

so, using given value,∪=0.05,

s = v2/2*0.05*g

We know, g = 10, so s = v² / (2*0.05*10) = v²

where v = initial velocity