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? express your answer in terms of v0

V=Vo

Explanation:

Lets take all car have same mass (m).

Given that

Initial Speed of 3m mass train  = Vo

Initial Speed of m mass train  = 2Vo

Initial Speed of 5m mass train  = 0

Lets take final speed of 5m mass train = V

Initial linear momentum Pi

Pi= 3m x Vo + m x 2Vo + 5m x 0

Pi=5 m Vo

The final linear momentum Pf

Pf= 5m x V

There is no any external force that is why linear momentum will be conserved

Pi=Pf

5 m Vo=5 m V

V=Vo

The speed of the  final car will be same as initial velocity of 3m cars.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s