To find the angular speed of the wheel at the end of the 2.60-s interval, we can use the equation for angular acceleration:
angular acceleration = (change in angular velocity) / (change in time)
In this case, the angular acceleration is given as -4.60 rad/s^2, and the change in time is 2.60 s. We need to find the change in angular velocity, which we can calculate using the formula:
change in angular velocity = angular acceleration * change in time
Plugging in the values,
change in angular velocity = -4.60 rad/s^2 * 2.60 s = -11.96 rad/s
Now, we need to find the initial angular velocity. We know that the wheel rotates through 85.4 rad in 2.60 s.
initial angular velocity = (change in angular displacement) / (change in time)
initial angular velocity = 85.4 rad / 2.60 s = 32.85 rad/s
Finally, to find the angular speed at the end of the interval, we add the initial angular velocity and the change in angular velocity:
angular speed = initial angular velocity + change in angular velocity
angular speed = 32.85 rad/s - 11.96 rad/s = 20.89 rad/s
Therefore, the angular speed of the wheel at the end of the 2.60-s interval is 20.89 rad/s.