13. The graph at right shows the angular velocity as a function of time

for the blade of a fan. The blade moves in a circular path.
a. If θ = 0 rad at t = 0 s, what is the blade’s position at t = 1.5 s?
b. At what time will the blade have completed 11 revolutions?

Please show the graph or data representing the graph.

To answer these questions, we need to understand the relationship between angular velocity and position in circular motion.

a. To determine the blade's position at t = 1.5 s, we first need to find the area under the curve of the graph from t = 0 s to t = 1.5 s. This area represents the change in angular displacement (θ).

To calculate the area, we divide the time interval into small intervals and find the corresponding angular displacements for each interval. Then we sum up all these small angular displacements to get the total angular displacement.

Since the graph represents angular velocity (ω) as a function of time (t), we need to use the relationship between angular displacement (θ) and angular velocity (ω):

θ = ∫ω dt

Integrating the angular velocity over the time interval (0 to 1.5 s), we get:

θ = ∫ω dt from 0 to 1.5

b. To determine the time when the blade completes 11 revolutions, we need to find the time at which the angle θ equals 11 revolutions (22π radians).

Similarly, we need to integrate the angular velocity over the time interval (0 to t) to find the corresponding angular displacement (θ):

θ = ∫ω dt from 0 to t

Then we can set the value of θ equal to 22π radians and solve for t.

Please provide the actual values of the angular velocity as a function of time graph to calculate the answers precisely.