1. **State the problem:** A wheel starts from rest and rotates with a constant angular acceleration of 5 rad/s² for 6 seconds. We need to find: a. Final angular velocity b. Angular displacement 2. **Formulas used:** - Final angular velocity: $$\omega = \omega_0 + \alpha t$$ - Angular displacement: $$\theta = \omega_0 t + \frac{1}{2} \alpha t^2$$ where: - $\omega_0$ is the initial angular velocity (rad/s) - $\alpha$ is the angular acceleration (rad/s²) - $t$ is the time (s) - $\omega$ is the final angular velocity (rad/s) - $\theta$ is the angular displacement (rad) 3. **Given values:** - $\omega_0 = 0$ (starts from rest) - $\alpha = 5$ rad/s² - $t = 6$ s 4. **Calculate final angular velocity:** $$\omega = 0 + 5 \times 6 = 30 \text{ rad/s}$$ 5. **Calculate angular displacement:** $$\theta = 0 \times 6 + \frac{1}{2} \times 5 \times 6^2 = \frac{1}{2} \times 5 \times 36 = \frac{1}{2} \times 180 = 90 \text{ rad}$$ 6. **Final answers:** - Final angular velocity: $30$ rad/s - Angular displacement: $90$ rad