If the velocity of a moving object doubles, what happens to its momentum?

It doubles
Momentum= mass * velocity
when velocity doubles
momentum= 2*(velocity* mass)

Momentum is the product of mass and velocity

example let velocity of body A = 4 m/s and mass be m

1) initial momentum(p) = 4m

2) velocity double --- ( multiply be 2)
 so new velocity = (4*2) = 8 m/s\

so final  momentum(p) = 8m

CONCLUSION :

make as if mass of object which is m has a numerical value (take 1 N for instance)

Therefore initial p = 4 and final  p = 8    (for mass=1N)

it is valid saying that " FOR AN OBJECT OF CONSTANT MASS, MOMENT TUM DOUBLE WITH DOUBLING VELOCITY"

hope it was clear enough :)