To determine 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 north. - Displacement = +150 km (north direction is considered positive) 2. **Second Leg of the Trip**: The car then travels 50 kilometers south. - Displacement = -50 km (south direction is considered negative) 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**: 2 hours 2. **Time for the Second Leg**: 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: \[ \text{Average Velocity} = \frac{100 \text{ km (north)}}{3 \text{ hours}} \approx 33.33 \text{ km/h (north)} \] ### Step 5: Analyze the Options Now, let's look at the options provided: - A. 50 km/h north - B. 100 km/h north - C. 100 km/h south - D. 75 km/h north None of the options match our calculated average velocity of approximately 33.33 km/h north. However, if we consider the average speed (which is different from average velocity), we can calculate that as well. ### Step 6: Calculate Average Speed Average speed is defined as the total distance traveled divided by the total time taken. 1. **Total Distance**: - Distance for the first leg = 150 km - Distance for the second leg = 50 km - Total Distance = 150 km + 50 km = 200 km 2. **Average Speed**: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{200 \text{ km}}{3 \text{ hours}} \approx 66.67 \text{ km/h} \] ### Conclusion The average velocity of the car for the entire trip is approximately 33.33 km/h north, which is not listed in the options. The correct answer based on the average velocity calculation is not provided in the options, indicating a possible error in the question or options. ### Summary - Average velocity is calculated as total displacement divided by total time. - Total displacement for the trip is 100 km north. - Total time for the trip is 3 hours. - Average velocity is approximately 33.33 km/h north, which does not match any of the provided options. - Average speed, which is different from average velocity, is approximately 66.67 km/h. ### Revision Points - Average velocity considers direction and displacement, while average speed does not. - Always differentiate between total distance and total displacement. - Ensure to check if the options provided match the calculated values. - Understand the difference between average speed and average velocity for clarity in problems.