To determine the average velocity of the car over the entire trip, we need to follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Concept of Average Velocity Average velocity is defined as the total displacement divided by the total time taken. Displacement is the straight-line distance from the starting point to the final position, along with the direction. ### Step 2: Calculate Total Displacement 1. **First Leg of the Trip:** - The car travels **150 kilometers north**. - Displacement for this leg = +150 km (we consider north as the positive direction). 2. **Second Leg of the Trip:** - The car then travels **50 kilometers south**. - Displacement for this leg = -50 km (south is considered the negative direction). 3. **Total Displacement:** \[ \text{Total Displacement} = 150 \text{ km (north)} - 50 \text{ km (south)} = 100 \text{ km (north)} \] ### Step 3: Calculate Total Time 1. **Time for the First Leg:** - The car takes **2 hours** to travel north. 2. **Time for the Second Leg:** - The car takes **1 hour** to travel south. 3. **Total Time:** \[ \text{Total Time} = 2 \text{ hours} + 1 \text{ hour} = 3 \text{ hours} \] ### Step 4: Calculate Average Velocity Now that we have both total displacement and total time, we can calculate the average velocity using the formula: \[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \] Substituting the values we calculated: \[ \text{Average Velocity} = \frac{100 \text{ km (north)}}{3 \text{ hours}} \approx 33.33 \text{ km/h (north)} \] ### Step 5: Analyze the Options Now, let's compare our calculated average velocity with the provided options: - A. 50 km/h north - B. 25 km/h north - C. 100 km/h north - D. 75 km/h south None of the options match our calculated average velocity of approximately 33.33 km/h north. Therefore, it seems there was an error in the recorded correct option. ### Step 6: Why Other Options Are Incorrect - **Option A (50 km/h north):** This is incorrect because it does not account for the total displacement and time correctly. The average velocity is lower than this value. - **Option B (25 km/h north):** This is also incorrect as it underestimates the average velocity based on the total displacement and time. - **Option C (100 km/h north):** This is incorrect because it suggests a much higher average velocity than what is calculated. - **Option D (75 km/h south):** This is incorrect as it indicates a southward direction, which does not reflect the overall displacement of 100 km north. ### Common Pitfalls - **Confusing Distance with Displacement:** Remember that distance is the total path traveled, while displacement is the straight-line distance from the start to the end point, considering direction. - **Ignoring Direction:** Always pay attention to the direction when calculating displacement, as it affects the sign of the value. ### Revision Summary - Average velocity is calculated as total displacement divided by total time. - Total displacement considers direction; in this case, it was 100 km north. - Total time for the trip was 3 hours. - The average velocity calculated was approximately 33.33 km/h north, which does not match the provided options. In conclusion, the correct average velocity for the car's trip is approximately 33.33 km/h north, and the recorded correct option of A (50 km/h north) is incorrect.