Answer:
θ = 33.54 rad
Explanation:
This is a circular motion exercise
θ= θ₀ + w₀ t + ½ α t²
suppose that for t = 0 the body is at its initial point θ₀ = 0 and from the graph we see that the initial angular velocity w₀ = -9.0 rad / s
we look for the angular acceleration,
α =
from the graph taken two points
α =
α = 3 rad / s²
we substitute in the first equation
θ = 0 -9 t + ½ 3 t²
the displacement is requested for t = 8.6 s
θ = = -9 8.6 + 3/2 8.6²
θ = 33.54 rad