A4.0-kilogram ball moving at 8.0 m/s to the right collides with a 1.0-kilogram ball at rest. after the collision, the 4.0-kilogram ball moves at 4.8 m/s to the right. what is the velocity of the 1-kilogram ball?

Its about momentum. Momentum (p)=mass(m)xvelocity(v)
So for the first ball P=4x8=32kgm/s
For the second the momentum is zero as it is still.
So overall momentum its 32kgm/s
Momentum has to be conserved
After the collision the momentum of the 4kg ball is 4x4.8=19.2kgm/s
As momentum is conserved 32-19.2=12.8kgm/s remaining
So rearrange for velocity so v=p/m=12.8/1=12.8m/s for the 1kg ball