A child is riding their big wheel around the neighborhood. They start by riding east for 92 meters. They turn north and ride 28 meters. They turn south and continue for 54 meters. Finally, they turn west and ride 92 meters. It takes the child 9 minutes.

What is the velocity of the child?

To determine the velocity of the child, we need to consider two key components: the displacement of the child and the time taken. Velocity is a vector quantity, meaning it considers both magnitude (speed) and direction, and is defined as:

\[
\text{Velocity} = \frac{\text{Displacement}}{\text{Time}}
\]

### Step 1: Determine the Displacement
Displacement is the straight-line distance from the starting point to the final position of the child.

- The child starts by riding east for 92 meters.
- They then turn north and ride 28 meters.
- Next, they turn south and ride 54 meters.
- Finally, they turn west and ride 92 meters.

#### Calculate the Net Displacement:
1. **East-West Direction**: The child rides 92 meters east and then 92 meters west, so the net displacement in the east-west direction is:
   \[
   92\, \text{m} - 92\, \text{m} = 0\, \text{m}
   \]

2. **North-South Direction**: The child rides 28 meters north and then 54 meters south, so the net displacement in the north-south direction is:
   \[
   28\, \text{m} - 54\, \text{m} = -26\, \text{m}
   \]
   (The negative sign indicates that the displacement is 26 meters to the south.)

So, the total displacement is 26 meters south.

### Step 2: Determine the Time Taken
The time taken is given as 9 minutes. Converting this to seconds:
\[
9\, \text{minutes} \times 60\, \text{seconds/minute} = 540\, \text{seconds}
\]

### Step 3: Calculate the Velocity
Since displacement is 26 meters south, and time is 540 seconds, the velocity is:
\[
\text{Velocity} = \frac{26\, \text{meters}}{540\, \text{seconds}} \approx 0.0481\, \text{m/s} \text{ south}
\]

### Final Answer:
The velocity of the child is approximately \( 0.0481 \, \text{m/s} \) to the south.

Would you like more details on any part of the solution? Here are some related questions you might find interesting:

1. How would the result change if the time taken was different?
2. What would the average speed be instead of velocity?
3. How is displacement different from distance traveled?
4. Can velocity be zero even if the child is moving?
5. What if the child had moved in a circular path instead?

**Tip:** Always remember that velocity considers the straight-line distance (displacement) and direction from the start to the end point, not the total distance traveled.

A child is riding their big wheel around the neighborhood. They start by riding east for 92 meters. They turn north and ride 28 meters. They turn south and continue for 54 meters. Finally, they turn west and ride 92 meters. It takes the child 9 minutes. What is the velocity of the child?

Learn how to calculate the velocity of a child riding a big wheel by analyzing displacement and time. This problem covers key kinematic concepts like displacement and velocity. Suitable for students in Grades 6-8.

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