What did I do wrong? (Newton's Second Law)

[glenohumeral13]

Homework Statement

(This is a problem I made up, so if the problem is with the problem, let me know.)
A 500N ball is being pushed down a carpeted decline of 24° to the horizontal. It starts from 1 m/s and ends the 20 foot (6.1 m) decline at 32 m/s. What is the coefficient and force of kinetic friction and applied force?

Homework Equations

I used:
F_g = ma_g, F = ma, a = μ_kg, and v_i = √(v_f² - (2ad)).

The Attempt at a Solution

F_g = ma_g
50N = m(9.81)
m = 5kg
v_i = √(v_f² - (2ad))
1 = √(32² - 2a(6.1))
1 = √(1024 - 12.2a)
1 = √(1011.8a)
1 = 38√(a)
1/38 = √(a)
.02² = a
a = .0004 m/s²
F = ma
F = 5*.0004
F = .002N
a = μ_kg
.0004 = μ_k(9.81)
μ_k = .000040775

 

[CWatters]

Does that value for "a" seem reasonable to you?

Spoiler

I know the equation as...

vf² = vi² + 2ad

2ad = vf² - vi²

a = (vf² - vi²)/2d

a = (1024 - 1) / (2*6.1)
= 84m/s²

 

[CWatters]

PS: It may not be your only error. I haven't checked.

 

[glenohumeral13]

Does that value for "a" seem reasonable to you?

Spoiler

I know the equation as...

vf² = vi² + 2ad

2ad = vf² - vi²

a = (vf² - vi²)/2d

a = (1024 - 1) / (2*6.1)
= 84m/s²

Thanks.