A3.0 kg cart moving due east at 4.0 m/s collides with a 6.0 kg cart moving due west. the carts stick together and come to rest after the collision. determine the initial speed of the 6.0 kg cart

The problem about describes a perfectly inelastic collision. We are tasked to find the initial velocity of an object having a mass of 6 kg moving due west. It is given in the problem that after collision the cart sticks together and it stops. Thus, the final mass is the sum of the two cart and the final velocity is zero. For a perfectly inelastic collision,

m1v1-m2v2=vf(m1+m2)
By Substitution,

3(4)-6(v2)=0
6v2=12
v2=2

Therefor, the initial velocity if a 6 kg cart is 2 m/s