Question

A puck of mass 300g is sliding along a friction-less patch of ice at 6.0m/s. It encounters a rough path of ice with the coefficient of friction of 0.1. How long will it take for the puck to stop and how far will it travel?

Answer 1

You can relate the distance it will travel \(d\) with the initial kinetic energy \(K_i\), using the Work-Energy theorem:
\[\Delta K = K_f - K_i = W_{net}\]
and considering that the only work to account for is the one made by the friction: \(W_{f}=f\times d\) with \(f=\mu mg\)
the final kinetic energy will be zero, since that determines the moment it stops
once you found \(d\) you can use kinematic to find the time it takes, you can calculate the acceleration knowing that the only force applied in the horizontal direction is friction.