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Three coupled railroad cars roll along and couple with a fourth car, which is initially at rest. These four cars roll along and couple with a fifth car initially at rest. This process continues until the speed of the final collection of railroad cars is one-fifth the speed of the initial three railroad cars. All the cars are identical. how many cars are in the final collection?

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Answer:

n=15

Explanation:

First of all let's define all the variables,

The total number of cars is given by n

The initial speed of the three cars is v

The final speed of all cars is [tex]\frac {v} {5}[/tex]

The mass of each car is m

So applying the conservation of the moment, we have

[tex]3mv + mv_1 + mv_2 .... = n (m) \frac {v} {5}[/tex]

as [tex]v_2 = v_3 = v_4 ... = 0m / s[/tex],

We have to,

[tex]3mv = n (m) \frac {v} {5}[/tex]

n = 15

The total number of cars is 15

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