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 average speed and average velocity. ### 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. Using the same formula for average velocity (v_avg): \[ v_{\text{avg}} = \frac{\text{Total Displacement}}{\text{Total Time}} \] Here: - Total Displacement = 150 kilometers east - Total Time = 2 hours Substituting the values: \[ v_{\text{avg}} = \frac{150 \text{ km east}}{2 \text{ h}} = 75 \text{ km/h east} \] ### Conclusion Thus, the car's average speed is **75 km/h**, and its average velocity is **75 km/h east**. ### Explanation of the Correct Option The correct option is **A. 75 km/h and 75 km/h east**. This option accurately reflects both the average speed and average velocity calculated above. ### Explanation of Other Options - **B. 150 km/h and 75 km/h east**: This option incorrectly states the average speed as 150 km/h. The average speed is calculated to be 75 km/h, not 150 km/h. - **C. 75 km/h and 75 km/h**: This option correctly states the average speed but omits the direction for average velocity. Average velocity must include direction (east in this case) to be complete. - **D. 150 km/h and 150 km/h east**: This option incorrectly states both the average speed and average velocity as 150 km/h. The calculations show that both values are actually 75 km/h. ### 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. **Ignoring Direction**: When calculating average velocity, always include the direction of displacement. 3. **Miscalculating Time or Distance**: Ensure that the values for distance and time are correctly interpreted and used in calculations. ### 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. - The car's average speed is 75 km/h, and its average velocity is 75 km/h east. - Always differentiate between scalar (speed) and vector (velocity) quantities in physics.