To find the acceleration of the motorcycle, we will use the formula for acceleration:
[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, and
- [tex]\( t \)[/tex] is the time over which the change in velocity occurs.
Let's go through the values given in the problem:
- The initial velocity ([tex]\(v_i\)[/tex]) of the motorcycle is [tex]\(15\)[/tex] meters/second.
- The final velocity ([tex]\(v_f\)[/tex]) of the motorcycle is [tex]\(24\)[/tex] meters/second.
- The time ([tex]\(t\)[/tex]) over which the velocity change occurs is [tex]\(3\)[/tex] seconds.
Now we substitute these values into the formula:
[tex]\[ a = \frac{24 \, \text{m/s} - 15 \, \text{m/s}}{3 \, \text{s}} \][/tex]
Perform the subtraction in the numerator:
[tex]\[ a = \frac{9 \, \text{m/s}}{3 \, \text{s}} \][/tex]
Then, perform the division:
[tex]\[ a = 3 \, \text{m/s}^2 \][/tex]
So, the acceleration of the motorcycle is [tex]\(3\)[/tex] meters per second squared. This corresponds to the numerical value associated, which is:
[tex]\[ 3 \, \text{m/s}^2 \][/tex]
Therefore, the correct answer is:
E. [tex]\(3 \, m/s^2\)[/tex]
