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:
![s=ut+\frac{1}{2}at^2](https://tex.z-dn.net/?f=s%3Dut%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
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
where L is the length of one car.
The same equation can be written considering the first 7 cars:
![7L = ut+\frac{1}{2}at'^2](https://tex.z-dn.net/?f=7L%20%3D%20ut%2B%5Cfrac%7B1%7D%7B2%7Dat%27%5E2)
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
![a=0.08L](https://tex.z-dn.net/?f=a%3D0.08L)
Substituting into the equation, we can find t':
![7L = \frac{1}{2}(0.08L)t'^2\\7=0.04t'^2\\t'=\sqrt{\frac{7}{0.04}}=13.2 s](https://tex.z-dn.net/?f=7L%20%3D%20%5Cfrac%7B1%7D%7B2%7D%280.08L%29t%27%5E2%5C%5C7%3D0.04t%27%5E2%5C%5Ct%27%3D%5Csqrt%7B%5Cfrac%7B7%7D%7B0.04%7D%7D%3D13.2%20s)
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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