To determine the average speed and average velocity of the car that travels 150 kilometers to the east in 2 hours, we need to understand the definitions of these two concepts and how to calculate them. ### Step 1: Calculate Average Speed **Average Speed** is defined as the total distance traveled divided by the total time taken. The formula for average speed (v_avg) is: \[ v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \] In this case: - Total Distance = 150 kilometers - Total Time = 2 hours Now, substituting the values into the formula: \[ v_{\text{avg}} = \frac{150 \text{ km}}{2 \text{ h}} = 75 \text{ km/h} \] ### Step 2: Calculate Average Velocity **Average Velocity** is defined as the total displacement divided by the total time taken. Displacement is the straight-line distance from the initial position to the final position, along with the direction. Since the car travels 150 kilometers to the east, the displacement is also 150 kilometers to the east. The formula for average velocity (v_avg) is: \[ v_{\text{avg}} = \frac{\text{Total Displacement}}{\text{Total Time}} \] In this case: - Total Displacement = 150 kilometers east - Total Time = 2 hours Now, substituting the values into the formula: \[ v_{\text{avg}} = \frac{150 \text{ km east}}{2 \text{ h}} = 75 \text{ km/h east} \] ### Conclusion From our calculations: - The average speed of the car is **75 km/h**. - The average velocity of the car is **75 km/h east**. Thus, the correct option is **A**: Average speed is 75 km/h, average velocity is 75 km/h east. ### Explanation of Other Options - **Option B**: Average speed is 75 km/h, average velocity is 150 km/h east. - This option incorrectly states the average velocity. The average velocity cannot exceed the average speed, as both are calculated based on the same distance and time. The average velocity is 75 km/h east, not 150 km/h. - **Option C**: Average speed is 75 km/h, average velocity is 0 km/h. - This option is incorrect because average velocity is not zero. The car has moved a significant distance (150 km east), so the average velocity is not zero. Average velocity is only zero if the initial and final positions are the same, which is not the case here. - **Option D**: Average speed is 150 km/h, average velocity is 150 km/h east. - This option is incorrect because it miscalculates the average speed. The average speed is 75 km/h, not 150 km/h. The average velocity also cannot exceed the average speed. ### Common Pitfalls 1. **Confusing Speed and Velocity**: Remember that speed is a scalar quantity (only magnitude), while velocity is a vector quantity (magnitude and direction). 2. **Misunderstanding Displacement**: Displacement is not the same as distance. Displacement considers the shortest path between the starting and ending points, including direction. 3. **Ignoring Units**: Always ensure that the units are consistent when performing calculations (e.g., kilometers and hours). ### Revision Summary - Average speed is calculated as total distance divided by total time. - Average velocity is calculated as total displacement divided by total time, including direction. - For this problem, both average speed and average velocity are 75 km/h, with the latter having a directional component (east). - Be careful to distinguish between distance (scalar) and displacement (vector) in physics problems.