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Does this chart show constant acceleration

To determine if the chart indicates constant acceleration, we can analyze the data by checking if the change in velocity (rate of change of position \(y\)) with respect to time \(t\) is constant. This would imply constant acceleration.

### Steps:
1. **Calculate velocities** for each interval by using the formula:
   \[
   v = \frac{\Delta y}{\Delta t}
   \]
   where \( \Delta y \) is the change in position and \( \Delta t \) is the change in time.
   
2. **Check if the change in velocity is constant** across different time intervals. If it is, then the chart reflects constant acceleration.

Let me calculate the velocities and check this condition.The analysis shows the following results:

- **Velocities (m/s) for each time interval:**
  \[
  1.24, 1.68, 2.22, 2.76, 3.24, 3.74, 4.26, 4.74, 5.36
  \]
- **Acceleration (m/s²)** (difference in velocities):
  \[
  0.44, 0.54, 0.54, 0.48, 0.50, 0.52, 0.48, 0.62
  \]

The accelerations are not perfectly constant but are relatively close, indicating that the system is experiencing **near constant acceleration** with minor variations.

Would you like further details or to explore something specific from this analysis?

Here are five related questions:
1. How can we calculate the average acceleration over the entire interval?
2. What might cause slight variations in the calculated accelerations?
3. Can we determine the equation of motion for this data?
4. How can we estimate the maximum velocity achieved in this data?
5. How do we experimentally verify constant acceleration?

**Tip:** To get a smooth acceleration curve, increasing the precision of measurements or accounting for external factors can help!

Does this chart show constant acceleration?

This problem explores the concept of constant acceleration using a position-time chart. By calculating velocities for each time interval and analyzing the change in velocity, we determine whether acceleration is constant. Suitable for students in Grades 9-12.

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