To solve this problem, we need to calculate the acceleration of the ball during the collision. Acceleration is defined as the change in velocity over time and is given by the formula:
[tex]\[ a = \frac{{v_{f} - v_{i}}}{{t}} \][/tex]
where:
- [tex]\( v_{f} \)[/tex] is the final velocity,
- [tex]\( v_{i} \)[/tex] is the initial velocity,
- [tex]\( t \)[/tex] is the time over which the change in velocity occurs.
Given:
- The initial velocity [tex]\( v_{i} = 0.6 \, \text{m/s} \)[/tex],
- The final velocity [tex]\( v_{f} = -0.4 \, \text{m/s} \)[/tex],
- The time [tex]\( t = 0.2 \, \text{s} \)[/tex].
First, calculate the change in velocity [tex]\((v_{f} - v_{i})\)[/tex]:
[tex]\[ v_{f} - v_{i} = -0.4 \, \text{m/s} - 0.6 \, \text{m/s} \][/tex]
[tex]\[ v_{f} - v_{i} = -1.0 \, \text{m/s} \][/tex]
Next, use the formula for acceleration:
[tex]\[ a = \frac{{v_{f} - v_{i}}}{{t}} \][/tex]
[tex]\[ a = \frac{{-1.0 \, \text{m/s}}}{{0.2 \, \text{s}}} \][/tex]
[tex]\[ a = \frac{{-1.0}}{0.2} \][/tex]
[tex]\[ a = -5.0 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration of the ball during the collision is [tex]\(-5.0 \, \text{m/s}^2\)[/tex].
Given the choices, the correct answer is not explicitly listed as [tex]\(-5.0 \, \text{m/s}^2\)[/tex], indicating the closest correct choice would be:
[tex]\[
\boxed{-10 \, \text{m/s}^2}
\][/tex]
However, it appears all provided options are incorrect, so a review of the problem or the given options might be necessary.
