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Three identical train cars, coupled together, are rolling east at speed v0. A fourth car traveling east at 2v0 catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train.What is the speed of the five-car train?

Answer :

Answer:[tex]v_o[/tex]

Explanation:

It is given that three cars has same mass m with speed [tex]v_o[/tex]

suppose rest two cars also has same mass m

As there is no external force therefore momentum is conserved

Initial Momentum [tex]P_i[/tex]

[tex]P_i=3mv_0+m(2v_0)+m\times 0[/tex]

Final momentum [tex]P_f[/tex]

[tex]P_f=5m\times v[/tex]

where v=final velocity

[tex]P_i=P_f[/tex]

[tex]5mv_o=5mv[/tex]

[tex]v=v_o[/tex]

thus final velocity is [tex]v_o[/tex]

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