Sin θ : 0.075, 0.111, 0.126, 0.141 
   Acceleration: -0.237, 0.624, 0.596, 0.605

Plot a graph of the average acceleration (y-axis) vs. sin(θ). Use LabQuest App, Logger Pro, or graph paper. Carry the horizontal axis out to sin(θ) = 1 (one) to leave room for extrapolation.  Draw a best-fit line by hand or use the proportional fit tool and determine the slope. The slope can be used to determine the acceleration of the cart on an incline of any angle.  On the graph, carry the fitted line out to sin(90°) = 1 on the horizontal axis and read the value of the acceleration.

Here is the graph of average acceleration versus \( \sin(\theta) \) with a best-fit line.

- The slope of the best-fit line is approximately 13.35.
- The y-intercept is around -1.11.

To find the acceleration at \( \sin(90^\circ) = 1 \), we can use the equation of the line:

\[
a = 13.35 \cdot \sin(\theta) - 1.11
\]

Substituting \( \sin(90^\circ) = 1 \):

\[
a = 13.35 \cdot 1 - 1.11 \approx 12.24 \, \text{m/s}^2
\]

This represents the extrapolated acceleration for \( \sin(90^\circ) \).

Do you want more details or have any questions?

Here are 5 follow-up questions for further exploration:
1. How does the slope relate to the acceleration on different inclines?
2. What physical significance does the y-intercept hold in this experiment?
3. How would the result change if air resistance were considered?
4. What assumptions are made about the incline and cart in this experiment?
5. How does the value of acceleration compare to gravitational acceleration?

**Tip**: To increase accuracy, ensure the measurement of \( \sin(\theta) \) and acceleration are as precise as possible, and consider multiple trials.

Sin θ : 0.075, 0.111, 0.126, 0.141 Acceleration: -0.237, 0.624, 0.596, 0.605. Plot a graph of the average acceleration (y-axis) vs. sin(θ). Use LabQuest App, Logger Pro, or graph paper. Carry the horizontal axis out to sin(θ) = 1 (one) to leave room for extrapolation. Draw a best-fit line by hand or use the proportional fit tool and determine the slope. The slope can be used to determine the acceleration of the cart on an incline of any angle. On the graph, carry the fitted line out to sin(90°) = 1 on the horizontal axis and read the value of the acceleration.

Learn how to plot a graph of acceleration vs. sin(θ) with a best-fit line and extrapolate to find the acceleration at sin(90°). This problem involves linear regression, trigonometry, and kinematics, providing insights into the motion of a cart on an incline. Suitable for high school students in Grades 10-12.

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