Two carts collide on a level, friction-less track. cart a has a mass of 200 g and is initially stationary. cart b has a mass of 100 g and is initially moving with a velocity of +2.0 m/s. after the collision between the carts, cart b has a velocity of -0.5 m/s.
calculate the velocity of cart a after the collision.
(use conservation of momentum, ke is not conserved.)

Convert 200 grams and 100 grams to 2kg and 1kg respectively 
momentum = mass x velocity 
momentum = 1 x 2 
initial momentum = 2 kg m/s
second scenario, cart b is moving -.5 m/s
momentum = mass x velocity
momentum = 1 x -.5
final momentum = -.5 kg m/s

momentum has to be the same in both scenarios so the 2 kg truck has to have a momentum of 2.5 kg m/s to push the total momentum of the second scenario to be 2 kg m/s like the first scenario

2.5 = 2 x velocity

velocity of cart a after the collision = 1.25 m/s