To find the acceleration of the train, we can use one of the basic kinematic equations that relates acceleration to the initial speed, final speed, and time. The formula for acceleration [tex]\(a\)[/tex] is given by:
[tex]\[ a = \frac{v_f - v_i}{t} \][/tex]
where:
- [tex]\( v_f \)[/tex] is the final speed,
- [tex]\( v_i \)[/tex] is the initial speed,
- [tex]\( t \)[/tex] is the time over which the change in speed occurs.
In this problem:
- The initial speed ([tex]\( v_i \)[/tex]) of the train is [tex]\( 5 \)[/tex] meters per second,
- The final speed ([tex]\( v_f \)[/tex]) is [tex]\( 45 \)[/tex] meters per second,
- The time ([tex]\( t \)[/tex]) taken to reach this final speed is [tex]\( 8 \)[/tex] seconds.
Substituting these values into the formula, we get:
[tex]\[ a = \frac{45 \, \text{m/s} - 5 \, \text{m/s}}{8 \, \text{s}} \][/tex]
[tex]\[ a = \frac{40 \, \text{m/s}}{8 \, \text{s}} \][/tex]
[tex]\[ a = 5 \, \text{m/s}^2 \][/tex]
Thus, the calculated acceleration is [tex]\( 5 \, \text{m/s}^2 \)[/tex].
Since the problem asks us to round the answer to the nearest whole number, we see that the calculated acceleration is already a whole number.
Therefore, the rounded acceleration of the train is [tex]\( 5 \, \text{m/s}^2 \)[/tex], which corresponds to the answer:
[tex]\[ \boxed{5 \, \text{m/s}^2} \][/tex]
