Final answer:
The angular acceleration of the tires is -0.14 rad/s².
Step-by-step explanation:
To find the angular acceleration of the tires, we can use the formula:
angular acceleration = (final angular velocity - initial angular velocity) / time
The initial and final angular velocities can be calculated using the formula:
angular velocity = linear velocity / radius
Given that the tires have a diameter of 0.88 m, their radius would be 0.88/2 = 0.44 m.
Converting the speeds from km/h to m/s:
Initial linear velocity = 94.0 km/h × (1000 m/1 km) × (1 h/3600 s) = 26.11 m/s
Final linear velocity = 64.0 km/h × (1000 m/1 km) × (1 h/3600 s) = 17.78 m/s
Substituting the values into the formulas:
Initial angular velocity = 26.11 m/s / 0.44 m = 59.34 rad/s
Final angular velocity = 17.78 m/s / 0.44 m = 40.41 rad/s
Time = Number of revolutions × (2π × radius) / linear velocity
Number of revolutions = (time × linear velocity) / (2π × radius)
Given that the number of revolutions is 88:
Angular acceleration = (40.41 rad/s - 59.34 rad/s) / ((88 × 2π × 0.44 m) / 17.78 m/s) = -0.14 rad/s²
Therefore, the angular acceleration of the tires is -0.14 rad/s².