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:
[tex]s=ut+\frac{1}{2}at^2[/tex]
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
[tex]a=\frac{2s}{t^2}=\frac{2L}{(5.0)^2}=0.08L[m/s^2][/tex]
where L is the length of one car.
The same equation can be written considering the first 7 cars:
[tex]7L = ut+\frac{1}{2}at'^2[/tex]
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
[tex]a=0.08L[/tex]
Substituting into the equation, we can find t':
[tex]7L = \frac{1}{2}(0.08L)t'^2\\7=0.04t'^2\\t'=\sqrt{\frac{7}{0.04}}=13.2 s[/tex]
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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