The force that must be applied to the train is [tex]-2.4\cdot 10^5 N[/tex]
Explanation:
First of all, we have to find the acceleration of the train. The motion of the train is a uniformly accelerated motion, so we can use the following suvat equation:
[tex]v=u+at[/tex]
where
v = 0 is the final velocity (it comes to a stop)
[tex]u=92 km/h =25.6 m/s[/tex] is the initial velocity
a is the acceleration
t = 85 s is the time elapsed
Solving for a, we find:
[tex]a=\frac{v-u}{t}=\frac{0-25.6}{85}=-0.30 m/s^2[/tex]
Where the negative sign means it is a deceleration.
Now we can find the force that must be applied to the train by using Newton's second law:
[tex]F=ma[/tex]
where
F is the force on the train
[tex]m=8.0\cdot 10^5 kg[/tex] is the mass of the train
[tex]a=-0.30 m/s^2[/tex] is the acceleration
Substituting,
[tex]F=(8.0\cdot 10^5)(-0.30)=-2.4\cdot 10^5 N[/tex]
Where the negative sign indicates that the force must be applied in a direction opposite to the motion of the train.
Learn more about acceleration and Newton's second law:
brainly.com/question/3820012
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