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