1. **State the problem:** A car travels along a straight path for 9 minutes with a given velocity-time graph. We need to find the total distance traveled by the car in kilometers, rounding to the nearest thousandth. 2. **Formula and concept:** Total distance traveled is the integral of the absolute value of velocity over time. Since velocity can be positive or negative, distance is the area under the velocity-time graph considering all areas as positive. 3. **Analyze the graph segments:** - From $t=0$ to $t=4$, velocity forms a semicircular arc peaking at $(2,2)$. - From $t=4$ to $t=5$, velocity decreases linearly from 0 to $-2$. - From $t=5$ to $t=9$, velocity increases linearly from $-2$ back to 0. 4. **Calculate area under semicircle (0 to 4):** The semicircle has radius $r=2$ (since it peaks at 2 km/min and spans from 0 to 4 min). Area of semicircle = $\frac{1}{2} \pi r^2 = \frac{1}{2} \pi (2)^2 = 2\pi$ km 5. **Calculate area of triangle (4 to 5):** Velocity drops from 0 to $-2$ km/min in 1 minute. Area = $\frac{1}{2} \times 1 \times 2 = 1$ km (take absolute value since velocity is negative) 6. **Calculate area of triangle (5 to 9):** Velocity rises from $-2$ to 0 km/min in 4 minutes. Area = $\frac{1}{2} \times 4 \times 2 = 4$ km (absolute value again) 7. **Sum all areas for total distance:** $$\text{Total distance} = 2\pi + 1 + 4 = 2\pi + 5$$ 8. **Numerical approximation:** $$2\pi \approx 6.283$$ So, $$\text{Total distance} \approx 6.283 + 5 = 11.283$$ km 9. **Final answer:** The total distance traveled by the car is approximately **11.283 km**.