Question

A child does a 12 j of work pushing his 3kg toy truck with what velocity does the toy move after the child done pushing

Answer 1

We have to assume that the truck was not moving
before he started pushing it.

After he did 12 J of work pushing it, the truck had
12 J of kinetic energy.

                                         Kinetic energy = (1/2) (mass) (speed²)

                                                12 J              =  (1/2) (3 kg) (speed²)

Divide each side by 1.5 kg :  12J / 1.5 kg = speed²

1 J = 1 newton-meter           (12 kg-m²/sec²) / (1.5 kg) = speed² 
      =  1 kg-m² / sec²                                     
                                               (12 / 1.5) ( m²/sec²)  =  speed²                                             

                                               Speed = √(8 m²/s²)

                                               Speed  =   2.83 m/s .

We can't say anything about velocity, because we don't know
anything about the direction in which the truck is moving.