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].
