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(1 point) The horizontal position of a car in a parking lot can be specified by providing its x and y coordinates. At time t = 0 s the car is located at x = y = 0 m. The Figure below shows the position of the car at 1 s intervals, starting from t = 0 s. It turns out that the x component of the velocity is constant. Use the Figure to estimate the magnitude of the x component of the velocity.

To estimate the magnitude of the \( x \)-component of the car's velocity from the graph:

1. **Observe the pattern**: The car moves along a parabolic trajectory, which suggests that the motion in the \( x \)-direction is uniform, while the \( y \)-direction varies, possibly due to gravitational effects.

2. **Use the data from the graph**:
   - The horizontal axis represents the \( x \)-coordinate (in meters), and the vertical axis represents the \( y \)-coordinate (in meters).
   - The graph shows that the car starts at \( x = 0 \) meters and reaches a maximum \( x \)-value of approximately 80 meters over a certain time period.

3. **Determine time**:
   - The car's position is plotted at **1-second intervals**.
   - By examining the graph, the car travels the full horizontal distance (from \( x = 0 \) to \( x \approx 80 \)) in approximately 10 seconds (assuming the total number of points corresponds to that duration).

4. **Calculate the \( x \)-component of the velocity**:
   - The horizontal displacement \( \Delta x \) is 80 meters, and the time interval \( \Delta t \) is 10 seconds.
   - The velocity \( v_x \) in the \( x \)-direction is calculated as:
   \[
   v_x = \frac{\Delta x}{\Delta t} = \frac{80 \, \text{m}}{10 \, \text{s}} = 8 \, \text{m/s}.
   \]

Thus, the magnitude of the \( x \)-component of the car's velocity is approximately **8 m/s**.

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Would you like further clarification or details? Here are some additional questions you might consider:

1. How can we determine the car's vertical velocity component?
2. Can we calculate the car's total velocity at specific points?
3. How does the parabolic motion in the graph relate to projectile motion principles?
4. What is the significance of the car's \( y \)-coordinate at different times?
5. Can we model the car's trajectory with a quadratic equation?

**Tip**: In projectile-like motions, horizontal velocity remains constant if there is no external force in the horizontal direction (like friction).

The horizontal position of a car in a parking lot can be specified by providing its x and y coordinates. At time t = 0 s the car is located at x = y = 0 m. The Figure below shows the position of the car at 1 s intervals, starting from t = 0 s. It turns out that the x component of the velocity is constant. Use the Figure to estimate the magnitude of the x component of the velocity.

Learn how to estimate the x-component of a car's velocity from a parabolic trajectory graph. This problem involves calculating horizontal velocity using kinematic principles. The car's motion is plotted at 1-second intervals, and the velocity is computed using the displacement over time. Suitable for Grades 9-12.

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