Answer :

Sure! To find the acceleration of the train, we will use the formula for acceleration:

[tex]\[ a = \frac{{v_f - v_i}}{t} \][/tex]

where:
- [tex]\( v_i \)[/tex] is the initial velocity
- [tex]\( v_f \)[/tex] is the final velocity
- [tex]\( t \)[/tex] is the time over which the change in velocity occurs

Let's break it down step by step:

1. Identify the given values:
- Initial velocity, [tex]\( v_i \)[/tex] = 20 m/s
- Final velocity, [tex]\( v_f \)[/tex] = 10 m/s
- Time, [tex]\( t \)[/tex] = 2 seconds

2. Substitute the given values into the acceleration formula:

[tex]\[ a = \frac{{10 \text{ m/s} - 20 \text{ m/s}}}{2 \text{ s}} \][/tex]

3. Perform the subtraction in the numerator:

[tex]\[ 10 \text{ m/s} - 20 \text{ m/s} = -10 \text{ m/s} \][/tex]

4. Divide the result by the time:

[tex]\[ a = \frac{{-10 \text{ m/s}}}{2 \text{ s}} = -5 \text{ m/s}^2 \][/tex]

So, the acceleration of the train is:

[tex]\[ a = -5 \text{ m/s}^2 \][/tex]

The negative sign indicates that the train is decelerating (slowing down). Therefore, the train's acceleration is [tex]\( -5 \text{ m/s}^2 \)[/tex].