Question

In another physics experiment, carts run along a frictionless, level track. Cart A is 1 kg and Cart B is 2 kg. Initially cart A is moving to the right at 2.0 m/s and cart B is moving to the left at 7.0 m/s. After they collide, Cart B is moving to the left at 3.5 m/s. What is the magnitude of the velocity of Cart A?

Answer 1

Answer:
`v_(f_A)` = 5 m/s

Explanation: For collisions, use linear momentum, whose formula is: P = m.v and knowing the law of conservation states that momentum of a closed system is constant in time, i.e. initial momentum equals final momentum:

`p_(f) = p_(i)`

`m_(A)v_(f_A) + m_(B)v_(f_B) = m_(A)v_(i_A) + m_(B)v_(i_B)`

Suppose the referential for velocity is positive to the right:

`1.v_(f_A) + 2.(-3.5) = 1.(+2) + 2.(-7)`

`1.v_(f_A) = 7 + 2 - 14`

`v_(f_A) = - 5`

The negative sign, in this case, indicates cart A is going to the left.

The magnitude of velocity of cart A is 5 m/s