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.