To find the acceleration of the ball, we can use the formula for acceleration:
\[ a = \frac{\Delta v}{\Delta t} \]
where:
- \(\Delta v\) is the change in velocity,
- \(\Delta t\) is the change in time.
In this case, the initial velocity (\(v_i\)) is 12 m/s, and the final velocity (\(v_f\)) is 0 m/s (since the ball comes to a stop). The time taken (\(\Delta t\)) is 3 seconds.
First, we calculate the change in velocity:
\[ \Delta v = v_f - v_i = 0 , \text{m/s} - 12 , \text{m/s} = -12 , \text{m/s} \]
Now, we can substitute \(\Delta v\) and \(\Delta t\) into the acceleration formula:
\[ a = \frac{-12 , \text{m/s}}{3 , \text{s}} = -4 , \text{m/s}^2 \]
The negative sign indicates that the acceleration is in the opposite direction of the velocity, which is expected since the ball is stopping.
Therefore, the acceleration of the ball is \(-4 , \text{m/s}^2\).
The correct response is:
- - 4 m/s²