A physics student obtains the following data involving a ball rolling down an inclined plane, where t is the elapsed time in seconds and y is the distance traveled in inches.

Question

t 0. 1. 2. 3. 4. 5
y. 0. 1.2 4.8 10.8 19.2. 30

Answer 1

To analyze the data provided for the ball rolling down an inclined plane, we will extract important details such as the distance traveled at different time intervals and analyze the relationship between time and distance.

Given Data

• Time (t) in seconds: 0, 1, 2, 3, 4, 5
• Distance (y) in inches: 0, 1.2, 4.8, 10.8, 19.2, 30

Steps to Analyze the Data:

1. Create a Table: We can tabulate the given data for clarity.

   | Time (s) | Distance (inches) | |:--------:|:-----------------:| | 0 | 0 | | 1 | 1.2 | | 2 | 4.8 | | 3 | 10.8 | | 4 | 19.2 | | 5 | 30.0 |

2. Calculate the Differences: We can find the change in distance for each second to see how the distance changes over time.

   | Time Interval (s) | Distance (inches) | Distance Change (inches) | |:------------------:|:-----------------:|:-------------------------:| | 0 to 1 | 1.2 | 1.2 | | 1 to 2 | 4.8 | 3.6 | | 2 to 3 | 10.8 | 6.0 | | 3 to 4 | 19.2 | 8.4 | | 4 to 5 | 30.0 | 10.8 |

3. Determine Acceleration: We can also calculate average velocities and acceleration between the intervals.

   The average velocity \( v \) during each interval can be calculated as: \[ v = \frac{\Delta y}{\Delta t} \]

   Using this, we can compute average velocities for each second as shown below.

   | Time Interval (s) | Distance Change (inches) | Average Velocity (inches/s) | |:------------------:|:-------------------------:|:----------------------------:| | 0 to 1 | 1.2 | 1.2 | | 1 to 2 | 3.6 | 3.6 | | 2 to 3 | 6.0 | 6.0 | | 3 to 4 | 8.4 | 8.4 | | 4 to 5 | 10.8 | 10.8 |

   Next, we can determine the average acceleration \( a \) using the formula: \[ a = \frac{\Delta v}{\Delta t} \] where \( \Delta v \) is the difference in average velocity over the time interval.

4. Plot the Data: If you were to plot this data, you would put time on the x-axis and distance on the y-axis. The trend should show a parabolic curve indicating accelerated motion as the ball rolls down the inclined plane.

Conclusion

The results indicate that as time progresses, the distance traveled increases at an increasing rate, which is characteristic of an object accelerating down an incline under the influence of gravity.

If you need specific calculations for acceleration or further analysis, please let me know!