Answer:
To calculate the average acceleration of the ball between points X and Y, you can use the following formula:
\[a_{\text{avg}} = \frac{{\Delta v}}{{\Delta t}}\]
Where:
- \(a_{\text{avg}}\) is the average acceleration.
- \(\Delta v\) is the change in velocity.
- \(\Delta t\) is the change in time.
Since the ball starts from rest, its initial velocity (\(v_i\)) is 0 m/s. We need to find the final velocity (\(v_f\)) and the time interval (\(\Delta t\)) between X and Y.
Given that the horizontal distance between X and Y is 0.060 m and we have positions at time intervals of 0.50 ms (which is 0.0005 seconds), we can calculate the final velocity using the formula:
\[v_f = \frac{{\Delta x}}{{\Delta t}}\]
Where:
- \(\Delta x\) is the change in position, which is 0.060 m.
- \(\Delta t\) is the time interval, which is 0.0005 seconds.
Now, calculate \(v_f\):
\[v_f = \frac{{0.060\, \text{m}}}{{0.0005\, \text{s}}} = 120\, \text{m/s}\]
Now that we have \(v_i = 0\, \text{m/s}\) and \(v_f = 120\, \text{m/s}\), you can calculate the average acceleration:
\[a_{\text{avg}} = \frac{{v_f - v_i}}{{\Delta t}} = \frac{{120\, \text{m/s} - 0\, \text{m/s}}}{{0.0005\, \text{s}}} = 240,000\, \text{m/s}^2\]
So, the average acceleration of the ball between X and Y is \(240,000\, \text{m/s}^2\).