Momentum principle:
Ft = mΔv
F: net force acting on the sled
t: time it takes from point A to point B (we're solving for this)
m: mass (this should cancel out after a few calculations, I'll show you how)
Δv: change in velocity from a to b
Δv = 5.0 - 8.0 = -3 m/s
Net force, F, can be broken down into two components: the component tangent (parallel) to the slope, and the friction force, which is normal (perpendicular) to the slope.
You can simply write F as μ*m*g when angle isn't given, the following two paragraphs are just a long explanation as to why that's the case.
F can be broken down into F-tangent, F-friction
F-tangent = m*g*sinθ (mass of sled times gravity to represent gravitational force, then sinθ to find the tangential component
F-friction = μ*F-normal (μ: coefficient of friction; μ = 0.25)
F-normal = m*g*cosθ (gravitational force, then cosθ to find the normal component)
F-friction = μ*m*g*cosθ; F-tangent = m*g*sinθ
Now, since both F-friction and F-tangent are acting on the sled, the effects of sinθ and cosθ cancel each other out.
F = μ*m*g
Substituting μ*m*g for F into the equation Ft = mΔv,
μ*m*g*t = m*Δv
Mass cancels out (when mass isn't given, it usually cancels out in equations)
μ*g*t = Δv
Variables we know: μ = 0.25; g = 9.81 m/s^2, Δv = -3 m/s
Now we can solve for t
0.25*9.81*t = -3
t = -3/(0.25*9.81)
t = -1.223 s
Since time can't be negative, the negative sign is meaningless here.
It takes roughly 1.223 seconds from A to B