Recall the formula,
∆θ = ω₀ t + 1/2 α t ²
where ∆θ = angular displacement, ω₀ = initial angular speed (which is zero because the disk starts at rest), α = angular acceleration, and t = time. Solve for the acceleration with the given information:
50 rad = 1/2 α (5 s)²
α = (100 rad) / (25 s²)
α = 4 rad/s²
Now find the angular speed ω after 3 s using the formula,
ω = ω₀ + α t
ω = (4 rad/s²) (3 s)
ω = 12 rad/s
