To find the average velocity of the car for 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 to the east. - Displacement = +150 km (east direction is considered positive) 2. **Second Leg of the Trip**: The car then returns 50 kilometers to the west. - Displacement = -50 km (west direction is considered negative) 3. **Total Displacement**: \[ \text{Total Displacement} = 150 \text{ km (east)} - 50 \text{ km (west)} = 150 \text{ km} - 50 \text{ km} = 100 \text{ km (east)} \] ### Step 3: Calculate Total Time 1. **Time for the First Leg**: The car travels for 2 hours. 2. **Time for the Second Leg**: The car returns in 1 hour. 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: \[ \text{Average Velocity} = \frac{100 \text{ km (east)}}{3 \text{ hours}} \approx 33.33 \text{ km/h (east)} \] ### Step 5: Rounding and Final Answer Since the options provided are in whole numbers, we can round 33.33 km/h to the nearest whole number, which is approximately 30 km/h. However, since the direction is east, we need to check the options carefully. ### Step 6: Evaluate the Options - **A. 50 km/h east**: This is incorrect because the average velocity we calculated is much lower than this value. - **B. 40 km/h east**: This is also incorrect as our calculated average velocity is approximately 33.33 km/h. - **C. 20 km/h east**: This is incorrect as it is significantly lower than our calculated average velocity. - **D. 30 km/h west**: This is incorrect because the average velocity is in the east direction, not west. ### Conclusion The correct average velocity for the entire trip is approximately 33.33 km/h east. However, since none of the options match this exactly, it seems there may have been an error in the options provided. The closest option to our calculation is **D. 30 km/h west**, but it is still incorrect due to the direction. ### Revision Summary - Average velocity is total displacement divided by total time. - Displacement considers direction; east is positive, west is negative. - Total displacement for the trip was 100 km east, and total time was 3 hours. - Average velocity calculated was approximately 33.33 km/h east, which does not match the provided options.