Given
Mass of the sled - m
Initial speed of the the sled - v
Coefficient of kinetic friction - µk
Acceleration due to gravity - g
Solution
The normal force acting on the object
N = mg
The friction resisting the movement
F = µkN
F = µkmg
The initial kinetic energy
E = ½ mv2
The friction will resist the movement of the sled, but the sled will try and move as long as it can perform the work against friction. It will come to rest when all of its kinetic energy is spent on doing work against friction
Work done = energy spent
W = E
Fd = E
µkmgd = ½ mv2
d = v2/2µkg
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