To find the average velocity of the car for the entire journey, we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Journey The car travels in two segments: 1. **First Segment**: 150 kilometers north in 2 hours. 2. **Second Segment**: 50 kilometers south in 1 hour. ### Step 2: Calculate Total Displacement Displacement is the overall change in position from the starting point to the final position, taking direction into account. - **Displacement from the first segment**: 150 km north. - **Displacement from the second segment**: 50 km south. To find the total displacement, we can treat north as positive and south as negative: - Total Displacement = Displacement from the first segment - Displacement from the second segment - Total Displacement = 150 km (north) - 50 km (south) = 150 km - 50 km = 100 km north. ### Step 3: Calculate Total Time Next, we need to calculate the total time taken for the journey: - Time for the first segment = 2 hours. - Time for the second segment = 1 hour. Total Time = Time for the first segment + Time for the second segment Total Time = 2 hours + 1 hour = 3 hours. ### Step 4: Calculate Average Velocity Average velocity is defined as the total displacement divided by the total time taken. The formula for average velocity (\(v_{avg}\)) is: \[ v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \] Substituting the values we calculated: \[ v_{avg} = \frac{100 \text{ km (north)}}{3 \text{ hours}} \approx 33.33 \text{ km/h (north)} \] ### Step 5: Analyze the Options Now, let's look at the options provided: - A. 50 km/h north - B. 66.67 km/h north - C. 100 km/h north - D. 100 km/h south ### Step 6: Evaluate Each Option - **Option A (50 km/h north)**: This is incorrect because the average velocity calculated is approximately 33.33 km/h, not 50 km/h. - **Option B (66.67 km/h north)**: This is incorrect as well; our calculation shows the average velocity is approximately 33.33 km/h, not 66.67 km/h. - **Option C (100 km/h north)**: This is also incorrect; the average velocity is not 100 km/h. - **Option D (100 km/h south)**: This is incorrect because the average velocity is positive (north), and the magnitude is not 100 km/h. ### Conclusion None of the options provided match the calculated average velocity of approximately 33.33 km/h north. Therefore, it seems there may have been an error in the options given or the expected answer. ### Revision Summary - Average velocity is calculated using total displacement divided by total time. - Displacement considers direction; north is positive, and south is negative. - The total displacement for the journey was 100 km north, and the total time was 3 hours. - The average velocity calculated was approximately 33.33 km/h north, which does not match any of the provided options. Make sure to double-check the options in your exam, as they may contain errors or misinterpretations.