If a 400g cart moving at 12 cm/s collides with an 800g cart at rest, what is their combined speed after the collision?

To determine the combined speed of the two carts after the collision, we can use the principle of conservation of momentum. Momentum before the collision must equal momentum after the collision.

First, we calculate the momentum of each cart before the collision:

• The momentum of the 400g cart moving at 12 cm/s is calculated as:

[

\text{Momentum} = \text{mass} \times \text{velocity} = 0.4 , \text{kg} \times 0.12 , \text{m/s} = 0.048 , \text{kg m/s}

]

• The 800g cart is at rest, so its momentum is:

[

0.8 , \text{kg} \times 0 , \text{m/s} = 0 , \text{kg m/s}

]

Adding these together gives the total momentum before the collision:

[

0.048 , \text{kg m/s} + 0 , \text{kg m/s} = 0.048 , \text{kg m/s}

]

After the collision, suppose the two carts