A 4.0-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