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This problem deals with a runner moving on a circular track and requires you to determine the direction of the average acceleration vector between two positions.

### Problem Breakdown:
- The runner is moving on a **circular track** of 400 m in circumference.
- The motion is **counterclockwise**, meaning the runner follows the track in a direction where their position changes as viewed from above.
- The runner starts on the **west side** at \( t = 0 \), and after some time, \( t = 19.06 \) s, the runner is at the **south end**.

Since the problem asks for the direction of the **average acceleration** between the runner's south position and west position, let's analyze:

#### Step 1: Understanding Position Change
- At \( t = 0 \), the runner is at the **west** side of the track.
- At \( t = 19.06 \) s, the runner is at the **south** side.
- The average acceleration is always directed towards the center of the path the object is traveling on. Since we are dealing with circular motion, the acceleration vector will point from one point of the circle towards the center.

#### Step 2: Determining the Average Acceleration Direction
- For **circular motion**, the **average acceleration** vector is directed along the line connecting the two positions.
  - **West** position to **South** position on a circle forms an arc between the west and south ends.
  - The **average acceleration vector** will point diagonally from the south position to the west position.
  
This diagonal lies in the **Northeast** direction.

### Correct Answer:
- The correct direction for the average acceleration vector is **Northeast (G)**.

Would you like further details or have any questions?

### Follow-up Questions:
1. How does average velocity differ from average acceleration in circular motion?
2. What is the formula for centripetal acceleration in circular motion?
3. Why does the direction of acceleration change in circular motion even if the speed is constant?
4. How does the time it takes to traverse a quarter of the circle relate to the speed of the runner?
5. How can you calculate the speed of the runner if you know the time and track circumference?

#### Tip:
In uniform circular motion, the direction of acceleration always points towards the center, while velocity is tangential to the circle at any given point.

A runner is running at speed v around a 400 m long circular track in a counterclockwise direction. At t = 0, he is on the west side of the track, and at time t = 19.06 s, he is at the south end of the track. What is the direction of his average acceleration (a vector) between his south position and his west position?

Determine the direction of average acceleration for a runner moving counterclockwise on a circular track, given time intervals and positions. This problem involves concepts of circular motion and vector analysis, suitable for Grades 10-12.

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