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?Express your answer in terms of v0

Answer 1

V=Vo

Step-by-step 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.