A car travels 120 meters north in 10 seconds and then instantly returns to its original position in the next 10 seconds. Which statement best describes the car's average velocity for the entire trip?

The correct option is: The average velocity is zero because the displacement is zero.

To understand why this is correct, we need to distinguish between two key concepts in physics: distance and displacement, as well as how they relate to speed and velocity.

1. Understanding Displacement
Displacement is a vector quantity that represents the net change in position of an object. It depends only on the starting position and the ending position, rather than the path taken:

$$\text{Displacement}=\text{Final Position}-\text{Initial Position}$$

In this scenario, the car starts at an initial position, travels 120 meters north, and then returns to its exact starting point (its original position). Because the final position is identical to the initial position, the overall displacement for the entire trip is:

$$\text{Displacement}=0\text{meters}$$

2. Calculating Average Velocity
Average velocity is defined as the total displacement divided by the total time taken for the trip:

$$v_{\text{avg}}=\frac{\text{Displacement}}{\text{Total Time}}$$

Substituting our values into the formula:

$$v_{\text{avg}}=\frac{0\text{m}}{20\text{s}}=0\text{m/s}$$

Therefore, because the displacement is zero, the average velocity for the entire trip is also zero.

3. Why other options are incorrect
Average speed is calculated using the total distance traveled (120 m + 120 m = 240 m) divided by total time (20 seconds), which yields 12 m/s. However, velocity specifically depends on displacement, not distance. Thus, calculations yielding non-zero values describe speed rather than average velocity.