Final answer:
The magnitude and direction of the total acceleration vector at the edge of the wheel at 1.0 s can be determined using the formulas for angular acceleration and magnitude of total acceleration.
Step-by-step explanation:
The magnitude and direction of the total acceleration vector at the edge of the wheel at 1.0 s can be determined using the formula:
angular acceleration = final angular velocity - initial angular velocity / time
Given that the wheel rotates from rest to 3 rev/s in 5 s, the initial angular velocity is 0 rad/s and the final angular velocity is 6π rad/s.
Substituting the values into the formula:
angular acceleration = (6π rad/s - 0 rad/s) / 5 s = 1.2π rad/s²
The magnitude of the total acceleration vector at the edge of the wheel can be calculated using the formula:
magnitude of total acceleration = radius × angular acceleration
Given that the radius of the wheel is 0.3 m:
magnitude of total acceleration = 0.3 m × 1.2π rad/s² ≈ 0.94 m/s²
Since the wheel starts from rest, the initial direction of the total acceleration vector is tangential.
Therefore, the correct answer is option C. 0.54 m/s², tangential.