Question

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 1

Answer:
`v_o`

Step-by-step explanation:

It is given that three cars has same mass m with speed
`v_o`

suppose rest two cars also has same mass m

As there is no external force therefore momentum is conserved

Initial Momentum
`P_i`

`P_i=3mv_0+m(2v_0)+m* 0`

Final momentum
`P_f`

`P_f=5m* v`

where v=final velocity

`P_i=P_f`

`5mv_o=5mv`

`v=v_o`

thus final velocity is
`v_o`