Answer:
The distance between the station A and B will be:
[tex]x_{A-B}=55.620\: km[/tex]
Explanation:
Let's find the distance that the train traveled during 60 seconds.
[tex]x_{1}=x_{0}+v_{0}t+0.5at^{2}[/tex]
We know that starts from rest (v(0)=0) and the acceleration is 0.6 m/s², so the distance will be:
[tex]x_{1}=\frac{1}{2}(0.6)(60)^{2}[/tex]
[tex]x_{1}=1080\: m[/tex]
Now, we need to find the distance after 25 min at a constant speed. To get it, we need to find the speed at the end of the first distance.
[tex]v_{1}=v_{0}+at[/tex]
[tex]v_{1}=(0.6)(60)=36\: m/s[/tex]
Then the second distance will be:
[tex]x_{2}=v_{1}*1500[/tex]
[tex]x_{2}=(36)(1500)=54000\: m[/tex]
The final distance is calculated whit the decelerate value:
[tex]v_{f}^{2}=v_{1}^{2}-2ax_{3}[/tex]
The final velocity is zero because it rests at station B. The initial velocity will be v(1).
[tex]0=36^{2}-2(1.2)x_{3}[/tex]
[tex]x_{3}=\frac{36^{2}}{2(1.2)}[/tex]
[tex]x_{3}=540\: m[/tex]
Therefore, the distance between the station A and B will be:
[tex]x_{A-B}=x_{1}+x_{2}+x_{3}[/tex]
[tex]x_{A-B}=1080+54000+540=55.620\: km[/tex]
I hope it helps you!
