Final velocity of this hockey puck

[Ace.]

Homework Statement

In the last second of a hockey game, a player slaps the puck in the empty net 32.5 m away. The puck leaves the stick with the speed of 41.5 m/s. Calculate the final velocity of the puck if its mass is 0.17 kg.

Homework Equations

μ_K = 0.005
μ_K = F_K / F_N
F = ma
v₂² = v₁² + 2ad

The Attempt at a Solution

Force normal of puck:
F_N = F_g = m x g

= 0.17 kg x 9.8 m/s²​

= 1.67 N​

μ_K = F_K / F_N
F_K = μ_K / F_N

= 0.005 / 1.67 N​

= 0.00835 N​

a = (F_unbalance/ m)

= (0.00835 N / 0.17 kg​

)

0.049 m/s²​

Finally, I solve for v₂:
v₂ = √(v₁² + 2ad)

= √(41.5² + 2(0.049)(32.5)​

= 41.5 m/s²​

My problem is that my final velocity is the same as my initial velocity? Where did I go wrong?

 

[superdave]

Well, you did do something wrong, but it won't affect your answer that much.

What direction is the acceleration going in?

 

[PhanthomJay]

You went wrong twice: first, your algebra error when calculating friction force, which should be uk(N). Then , watch your signage for acceleration when using the kinematic equations.

 

[Ace.]

I feel dumb, thanks.

 

[haruspex]

You have two problems.
The acceleration is so small that you have lost the change in velocity in the rounding error. On the other hand, if you show more digits in your answer then you will be guilty of gaining precision: you'll have more significant digits in the answer than in the provided data. So the short answer is the change in speed is negligible.
Your second problem is that you have acceleration going the wrong way. The dynamic friction seems to be making your puck go faster.