What is the velocity of an object of mass 10 kg that sticks to a stationary object of mass 5 kg when they collide and move together at 4 m/s?

When objects collide and the collision is inelastic the
total momentum is conserved though total kinetic energy may not be
conserved.

Here the objects collide and stick together, so
we can say that the collision is inelastic.

Let the initial
velocity of the object of mass 10 kg be V. The object of mass 5 kg is stationary and has
no momentum. The total momentum of the system initially is 10*V + 0 =
10*V.

After the objects collide, they move forward with a
velocity of 4 m/s. Therefore the momentum is (10 +5)*4 = 15*4 = 60
kg*m/s.

Equating the final momentum in the system to the
initial momentum we get

60 =
10*V

=> V =
60/10

=> V = 6
m/s

Therefore the original velocity of the moving object
was 6 m/s.