The time needed for the 7th car to pass is 13.2 s
Explanation:
The motion of the train is a uniformly accelerated motion, therefore we can use suvat equations.
We start by analzying the motion of the first car, by using the equation:

where
s is the distance covered by the first car in a time t, which corresponds to the length of one car
u = 0 is the initial velocity
a is the acceleration
t = 5.0 s is the time
The equation can be rewritten as
![a=\frac{2s}{t^2}=\frac{2L}{(5.0)^2}=0.08L[m/s^2]](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B2s%7D%7Bt%5E2%7D%3D%5Cfrac%7B2L%7D%7B%285.0%29%5E2%7D%3D0.08L%5Bm%2Fs%5E2%5D) 
 
where L is the length of one car.
The same equation can be written considering the first 7 cars:

where
7L is the distance covered by the 7 cars
t' is the time needed
We still have
u = 0
And the acceleration is constant so it is

Substituting into the equation, we can find t':

In attachment the graph of the distance covered versus the time taken: since the motion is uniformly accelerated, the relationship between the two variables is quadratical.
Learn more about accelerated motion:
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