1. **State the problem:** A motorcycle moves on a circular track of radius 500 m. It covers an arc length of 1.2 km in 3 minutes. We need to find: (a) The central angle in degrees. (b) Its speed in km/h. 2. **Formulas and rules:** - Arc length formula: $$s = r\theta$$ where $s$ is arc length, $r$ is radius, and $\theta$ is central angle in radians. - To convert radians to degrees: $$\theta_{degrees} = \theta_{radians} \times \frac{180}{\pi}$$ - Speed formula: $$\text{speed} = \frac{\text{distance}}{\text{time}}$$ 3. **Calculate central angle in radians:** Given $s = 1.2$ km = 1200 m, $r = 500$ m, $$\theta = \frac{s}{r} = \frac{1200}{500} = \frac{\cancel{1200}}{\cancel{500}} = 2.4 \text{ radians}$$ 4. **Convert central angle to degrees:** $$\theta_{degrees} = 2.4 \times \frac{180}{\pi} = \frac{2.4 \times 180}{3.1416} \approx 137.51^\circ$$ 5. **Calculate speed in km/h:** Distance = 1.2 km, Time = 3 minutes = $\frac{3}{60} = 0.05$ hours, $$\text{speed} = \frac{1.2}{0.05} = 24 \text{ km/h}$$ **Final answers:** (a) Central angle = $137.51^\circ$ (b) Speed = 24 km/h