To determine the acceleration of the rock, we use the following basic kinematic formula:
[tex]\[ a = \frac{{v_f - v_i}}{t} \][/tex]
Where:
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( v_f \)[/tex] is the final velocity,
- [tex]\( v_i \)[/tex] is the initial velocity,
- [tex]\( t \)[/tex] is the time.
Given:
- The initial velocity ([tex]\( v_i \)[/tex]) is [tex]\( 2.0 \, \text{m/s} \)[/tex],
- The final velocity ([tex]\( v_f \)[/tex]) is [tex]\( 44.0 \, \text{m/s} \)[/tex],
- The time ([tex]\( t \)[/tex]) is [tex]\( 12 \, \text{seconds} \)[/tex].
Now, let's substitute these values into the formula to find the acceleration:
[tex]\[ a = \frac{{44.0 \, \text{m/s} - 2.0 \, \text{m/s}}}{12 \, \text{seconds}} \][/tex]
[tex]\[ a = \frac{42.0 \, \text{m/s}}{12 \, \text{seconds}} \][/tex]
[tex]\[ a = 3.5 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration of the rock is [tex]\( 3.5 \, \text{m/s}^2 \)[/tex].
The correct answer is [tex]\( 3.5 \, \text{m/s}^2 \)[/tex].
