Let’s say you have a table of columns for a data that was for a ball, rolling down the hill, filling in the missing data values in the table and determine the acceleration of the rolling ball. Assume the patterns continues in both columns. Fill in the question marks.
Time seconds = 0 (start), 2, ?, ?, 8, 10 (end)
Velocity (m/s) = 0 (start), 3, 6, 9, ?, 15 (end
To determine the missing values and calculate the acceleration, we can observe the pattern in the Velocity column.
The time intervals between each recorded value in the Velocity column are constant. Based on this observation, we can calculate the missing time values.
From start to 2 seconds, the velocity increases by 3 m/s (0 to 3). This gives us a rate of change of 3 m/s per 2 seconds.
To find the missing time value after 2 seconds, we can apply this rate of change:
2 seconds + 2 seconds = 4 seconds
To find the next missing time value, we can again add 2 seconds:
4 seconds + 2 seconds = 6 seconds
Now, let's fill in the missing values in the table:
Time seconds = 0 (start), 2, 4, 6, 8, 10 (end)
Velocity (m/s) = 0 (start), 3, 6, 9, ??, 15 (end)
To determine the acceleration, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
For the given data:
Initial Velocity = 0 m/s
Final Velocity = 15 m/s
Time = 10 seconds
Acceleration = (15 - 0) / 10
Acceleration = 1.5 m/s^2
Therefore, the acceleration of the rolling ball is 1.5 m/s^2.