Think in terms of energy in the system ( draw a picture).
This isn't about rates. Don't think 12m/s * 3s =36m; "where'd we get 3 seconds?"; because that's not what's happening. We're wondering where is all the kinetic energy going from the inital state of movement to when there is no kinetic energy and it is at rest.
http://www.teachanddiscover.net/wiki/index.php/Friction_and_the_Normal_Force
100% kinetic energy is given and 0% kinetic energy is what we want because we want to know where it stops. But where did the energy go? Kinetic energy had to turn into something, it didn't just disappear right - it transferred to another form and the total energy in the system has to be the same because thermodynamics? So let's look at energy, which is measured in Joules.
Kinetic energy becomes Work done by friction
KE= work
1/2mv^2 = Force of friction x distance
The big F is the force of kinetic friction which is equal to the coefficient of kinetic friction times the normal force.
1/2mv^2 = ( coefficient of kinetic friction ) x (Normal Force) x distance
and normal force in the case of a horizontal surface the puck is sliding on is just the force opposing gravity, and force = mass x acceleration,
and since acceleration is not that of the puck but that of the normal force which is opposing gravity, a = gravitational acceleration magnitude = 9.8, in scalar terms
1/2mv^2 = (coefficient of kinetic friction) x (mass x gravity) x distance
mass can be canceled on both sides
YIELDING
0.5(144)=0.2(9.8)d
which is kinda like 72*5/10, which is like 72 * 0.5 = which is 36. no calc needed.
for other references, consult an introductory physics textbook or use google/wikipedia
